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Recent Advances in the Representation Theory of Finite Dimensional Algebras

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Representation Theory of Finite Groups and Finite-Dimensional Algebras

Part of the book series: Progress in Mathematics ((PM,volume 95))

Abstract

This is a report on advances in the representation theory of finite dimensional algebras in the years 1984 – 1990. During these years, the German research council (DFG) has sponsered a Forschungsschwerpunkt devoted to the representation theory of finite groups and finite dimensional algebras; it started in 1984 and will be finished by 1991.

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References

  1. Agoston, I.: Quotients of quasi-hereditary algebras. C. R. Math. Rep. Acad. Sci. Canada 11 (1989), 99–103.

    MathSciNet  MATH  Google Scholar 

  2. Assem, I.; Skowronski, A.: Iterated tilted algebras of type à n, Math. Z. 195 (1987), 269–290

    Article  MathSciNet  MATH  Google Scholar 

  3. Assem, I.; Skowronski, A.: On some classes of simply connected algebras. Proc. London Math. Soc. 56 (1988), 417–450.

    Article  MathSciNet  MATH  Google Scholar 

  4. Assem, I.; Skowronski, A.: Algebras with cycle finite derived categories. Math. Ann. 280 (1988), 441–463.

    Article  MathSciNet  MATH  Google Scholar 

  5. Assem, I.; Skowronski, A.: Algèbres pré-inclinées et catégories dérivées. In: Sém. d’Algèbre Dubreil-Malliavin. Springer LNM. 1404 (1989), 1–34.

    Chapter  Google Scholar 

  6. Assem, L; Skowronski, A.: Minimal representation-infinite coil algebras. Manuscr. Math. 67 (1990), 305–331.

    Article  MathSciNet  MATH  Google Scholar 

  7. Auslander, M.; Buchweitz, R.-O.: The homology theory of maximal Cohen-Macaulay approximations. Mém. Soc. Math. France N.S. (1989).

    Google Scholar 

  8. Auslander, M.; Platzeck, M. L; Todorov, G.: Homological theory of idempotent ideals. (To appear).

    Google Scholar 

  9. Auslander, M.; Reiten, I.: Applications of contravariantly finite subcategories. Preprint 8/1989 Univ. Trondheim.

    Google Scholar 

  10. Auslander, M.; Reiten, L: Cohen-Macaulay and Gorenstein Artin algebras. This volume.

    Google Scholar 

  11. Bakke, Ø.; Smalø, S.O.: Modules with the same socles and tops as a directing module are isomorphic. Comm. Algebra 15 (1987), 1–10.

    Article  MathSciNet  MATH  Google Scholar 

  12. Bautista, R.: On algebras of strongly unbounded representation type. Comment. Math. Helv. 60 (1985), 392–399.

    Article  MathSciNet  MATH  Google Scholar 

  13. Bautista, R.; Kleiner, M.: Almost split sequences for relatively projective modules. J. Algebra 135 (1990), 19–56

    Article  MathSciNet  MATH  Google Scholar 

  14. Baer, D.: Homological properties of wild hereditary Artin algebras. In: Representation Theory I. Springer LNM 1177 (1986), 1–12

    Google Scholar 

  15. Baer, D.: Wild hereditary Artin algebras and linear methods. Manuscr. Math. 55 (1986), 69–82.

    Article  MathSciNet  MATH  Google Scholar 

  16. Baer, D.: Tilting sheaves in representation theory of algebras. Manuscr. Math. 60 (1988), 323–347.

    Article  MathSciNet  MATH  Google Scholar 

  17. Baer, D.: A note on wild quiver algebras and tilting modules. Comm. Algebra 17 (1989), 751–757

    Article  MathSciNet  MATH  Google Scholar 

  18. Baer, D.; Geigle, W.; Lenzing, H.: The preprojective algebra of a tame hereditary Artin algebra. Comm. Algebra 15 (1987), 425–457.

    Article  MathSciNet  MATH  Google Scholar 

  19. Beilinson, A.; Ginsburg, V.: Mixed categories, Ext-duality abd representations (Results and conjectures). (To appear).

    Google Scholar 

  20. Benson, D.: Modular Representation Theory: New Trends and Methods. Springer LNM 1081 (1984).

    Google Scholar 

  21. Bessenrodt-Timmerscheidt, Ch.: The Auslander-Reiten quiver of a modular group algebra revisited. Preprint SM-DU-159 Duisburg (1989).

    Google Scholar 

  22. Bongartz, K.: Indecomposables are standard. Comment. Math. Helv. 60 (1985), 400–410.

    Article  MathSciNet  MATH  Google Scholar 

  23. Bongartz, K.; Smalø, S.O.: Modules determined by their tops and socles. Proc. Amer. Math. Soc. 96 (1986), 34–38.

    Article  MathSciNet  MATH  Google Scholar 

  24. Brenner. Sh.: A combinatorial characterization of finite Auslander-Reiten quivers. In: Representation Theory I. Springer LNM 1177 (1986), 13–49.

    Google Scholar 

  25. Bretscher, O; Todorov, G.: On a theorem of Nazarova and Roiter. In: Representation Theory I. Springer LNM 1177 (1986), 50–54.

    Google Scholar 

  26. Broué, M.: News about perfect isometries. (Unpublished).

    Google Scholar 

  27. Burt, W.L.; Butler, M.C.R.: Almost split sequences for bocses. (To appear).

    Google Scholar 

  28. Butler, M.C.R.; Ringel, C.M.: Auslander-Reiten sequences with few middle terms, with applications to string algebras. Comm. Alg. 15 (1987), 145–179.

    Article  MathSciNet  MATH  Google Scholar 

  29. Cline, E.; Parshall, B.; Scott, L.: Algebraic statification in representation categories. J. Algebra. 117 (1988), 504–521

    Article  MathSciNet  MATH  Google Scholar 

  30. Cline, E.; Parshall, B.; Scott, L.: Finite dimensional algebras and highest weight categories. J. reine angew. Math. 391 (1988), 85–99

    MathSciNet  MATH  Google Scholar 

  31. Cline, E.; Parshall, B.; Scott, L.: Duality in highest weight categories. In: Classical Groups and Related Topics. Contemp. Math. 82 (1989), 7–22.

    Article  MathSciNet  Google Scholar 

  32. Collingwood, D.H.; Irving, R.S.: A decomposition theorem for certain self-dual modules in the categorie O. Duke Math. J. 58 (1989), 89–102.

    Article  MathSciNet  MATH  Google Scholar 

  33. Crawley-Boevey, W.: On tame algebras and bocses. Proc. London Math. Soc. (3), 56 (1988), 451–483.

    Article  MathSciNet  MATH  Google Scholar 

  34. Crawley-Boevey, W.: Functorial filtrations and the problem of an idempotent and a square-zero matrix. J. London Math. Soc. (2) 38 (1988), 385–402.

    MathSciNet  MATH  Google Scholar 

  35. Crawley-Boevey, W.: Functorial filtrations II: Clans and the Gelfand problem. J. London Math. Soc. (2) 40 (1989), 9–30.

    Article  MathSciNet  MATH  Google Scholar 

  36. Crawley-Boevey, W.: Functorial filtrations III: Semi-dihedral algebras. J. London Math. Soc. (2) 40 (1989), 31–39.

    Article  MathSciNet  MATH  Google Scholar 

  37. Crawley-Boevey, W.: Maps between representations of zero-relation algebras. J. Algebra 126 (1989), 259–263

    Article  MathSciNet  MATH  Google Scholar 

  38. Crawley-Boevey, W.: Tame hereditary algebras, hereditary orders and their curves. (To appear).

    Google Scholar 

  39. Crawley-Boevey, W.: Matrix reduction for artinian rings, and an application to rings of finite representation type. Preprint 90-020 SFB 343 Bielefeld.

    Google Scholar 

  40. Crawley-Boevey, W.: Tame algebras and generic modules. Preprint 89-028 SFB 343 Bielefeld.

    Google Scholar 

  41. Crawley-Boevey, W.: Lectures at the Tsukuba Workshop 1990. (To appear).

    Google Scholar 

  42. Crawley-Boevey, W.; Ringel, C.M.: Algebras whose Auslander-Reiten components have large regular components. Preprint 90-052 SFB 343 Bielefeld.

    Google Scholar 

  43. Crawley-Boevey, W.; Unger, L.: Dimensions of Auslander-Reiten translates for representation-finite algebras. Comm. Algebra 17 (1989), 837–842.

    Article  MathSciNet  MATH  Google Scholar 

  44. D’Este, G.; Happel, D.: Representable equivalences are represented by tilting modules. Rend. Sem. Mat. Univ. Padova 82 (1990), 77–80.

    MathSciNet  Google Scholar 

  45. Dieterich, E.: Solution of a non-domestic tame classification problem from intergal representation theory of finite groups (Λ = RC 3, v(3)= A.) Memoirs Amer. Math. Soc. (To appear).

    Google Scholar 

  46. Dlab, V.; Ringel, C.M.: Quasi-hereditary algebras. Illinois J. Math. 33 (1989), 280–291

    MathSciNet  MATH  Google Scholar 

  47. Dlab, V.; Ringel, C.M.: Auslander algebras as quasi-hereditary algebras. J. London Math. Soc. (2) 39 (1989), 457–466.

    Article  MathSciNet  MATH  Google Scholar 

  48. Dlab, V.; Ringel, C.M.: Every semiprimary ring is the endomorphism ring of a projective module over a quasi-hereditary ring. Proc. Amer. Math. Soc. 107 (1989), 1–5.

    MathSciNet  MATH  Google Scholar 

  49. Dlab, V.; Ringel, C.M.: A construction for quasi-hereditary algebras. Compositio Math. 70 (1989), 155–175.

    MathSciNet  MATH  Google Scholar 

  50. Dlab, V.; Ringel, C.M.: The dimension of a quasi-hereditary algebra. In: Topics in Algebra. Banach Center Publ. 26. (To appear).

    Google Scholar 

  51. Dlab, V.; Ringel, C.M. Filtrat ions of right ideals related to projectivity of left ideals. In: Sém. d’Algèbre Dubreil-Malliavin. Springer LNM. 1404 (1989), 95–107.

    Chapter  Google Scholar 

  52. Dlab, V.; Ringel, C.M.: The Hochschild cocycle corresponding to a long exact sequence. Tsukuba J. Math (To appear).

    Google Scholar 

  53. Dlab, V.; Ringel, C.M.: Towers of semi-simple algebras. J. Funct. Anal. (To appear)

    Google Scholar 

  54. Dowbor, P.; Geigle, W.; Lenzing, H.: Graded Sheaf Theory and Group Quotients, with Applications to Representations of Finite Dimensional Algebras. (To appear).

    Google Scholar 

  55. Dowbor, P.; Meltzer, H.: On equivalences of Bernstein-Gelfand-Gelfand, Beilinson and Happel. Preprint 257 Humboldt-Universität Berlin (1990).

    Google Scholar 

  56. Dowbor, P.; Skowroński, A.: Galois coverings of representation-infinite algebras. Comment. Math. Helv. 62 (1987), 311–337.

    Article  MathSciNet  MATH  Google Scholar 

  57. Dräxler, P.: U-Fasersummen in darstellungsendlichen Algebren. J. Algebra 113 (1988), 430–437.

    Article  MathSciNet  MATH  Google Scholar 

  58. Dräxler, P.: Aufrichtige gerichtete Ausnahmealgebren. Bayreuther Math. Schriften 29 (1989).

    Google Scholar 

  59. Dräxler, P.: Fasersummen über dünnen s-Startmoduln. Arch. Math. 54 (1990), 252–257.

    Article  Google Scholar 

  60. Dräxler, P.: On indecomposable modules over directed algebras. (To appear).

    Google Scholar 

  61. Drinfeld, V.G.: Quantum groups. In: Proc. Intern. Congr. Math. 1986. Amer. Math. Soc. (1987), Vol.1, 798–820.

    MathSciNet  Google Scholar 

  62. Erdmann, K.: Tame Blocks and Related Algebras. Springer LNM 1428 (1990).

    MATH  Google Scholar 

  63. Erdmann, K.: On Auslander-Reiten components for wild blocks. This volume.

    Google Scholar 

  64. Erdmann, K.; Skowroñski, A.: On Auslander-Reiten components of blocks and self-injective biserial algebras. (To appear).

    Google Scholar 

  65. Fischbacher, U.: Une nouvelle preuve d’un théorème de Nazarova et Roiter. C.R. Acad. Sc. Paris I 300 (1985), 259–262.

    MathSciNet  MATH  Google Scholar 

  66. Fischbacher, U.; de la Peña, J.: Algorithms in representation theory of algebras. In: Representation Theory I. Springer LNM 1177 (1986), 94–114.

    Google Scholar 

  67. Gabriel, P.; de la Peña, J.: Quotients of representation-finite algebras. Comm. Algebra 15 (1987), 279–308.

    Article  MathSciNet  MATH  Google Scholar 

  68. Geigle, W.; Lenzing, H.: A class of weighted projective curves arising in the representation theory of finite dimensional algebras. In: Singularities, Representations of Algebras, and Vector Bundles. Springer LNM 1273 (1987), 265–297.

    Chapter  Google Scholar 

  69. Geigle, W.; Lenzing, H.: Perpendicular categories with applications to representations and sheaves. J. Algebra (To appear).

    Google Scholar 

  70. Green, J.A.: On certain subalgebras of the Schur algebra. (To appear).

    Google Scholar 

  71. Green, E.L.; Kirkman, E.; Kuzmanovich, J.: Finitistic dimension of finite dimensional monomial algebras. J. Algebra 136 (1991), 37–50.

    Article  MathSciNet  MATH  Google Scholar 

  72. Green, E.L.; Zimmermann-Huisgen, B.: Finitistic dimension of artinian rings with vanishing radical cube zero. Math. Z. (To appear).

    Google Scholar 

  73. Goodman, F.M., de la Harpe, P.; Jones, V.F.R.: Coxeter Graphs of Algebras. Math. Sci. Res. Inst. Publ. 14 (1989).

    Google Scholar 

  74. Guo, J.Y.: The isomorphism of Hall algebras. Preprint 90-060 SFB 343 Bielefeld.

    Google Scholar 

  75. Guo, J.Y.: The center of a Hall algebra. Preprint 90-061 SFB 343 Bielefeld.

    Google Scholar 

  76. Guo, J.Y.: The Hall algebra of a cyclic serial algebra. (In preparation)

    Google Scholar 

  77. Happel, D.: On the derived category of a finite-dimensional algebra. Comment. Math. Helv. 62 (1987), 339–389.

    Article  MathSciNet  MATH  Google Scholar 

  78. Happel, D.: Iterated tilted algebras of affine type. Comm. Alg. 15 (1987), 29–46

    Article  MathSciNet  MATH  Google Scholar 

  79. Happel, D.: Repetitive categories. In: Singularities, Representations of Algebras, and Vector Bundles. Springer LNM 1273 (1987), 298–317

    Chapter  Google Scholar 

  80. Happel, D.: Triangulated Categories in the Representation Theory of Finite-dimensional Algebras. London Math. Soc. LNS 119 (1988).

    Book  MATH  Google Scholar 

  81. Happel, D.: Hochschild cohomology of finite-dimensional algebras. In: Sérn. d’Algbre. Dubreil-Malliavin. Springer LNM 1404 (1989), 108–126.

    Chapter  Google Scholar 

  82. Happel, D.: A family of algebras with two simple modules and Fibonacci numbers. Archiv Math. (To appear)

    Google Scholar 

  83. Happel, D.: Partial tilting modules and recollement. Preprint 89-016 SFB 343 Bielefeld.

    Google Scholar 

  84. Happel, D.: Auslander-Reiten triangles in derived categories of finite-dimensional algebras. Proc. Amer. Math. Soc. (To appear).

    Google Scholar 

  85. Happel, D.: On Gorenstein algebras. This volume.

    Google Scholar 

  86. Happel, D.: Hochschild cohomology of Auslander algebras. In: Topics in Algebra. Banach Center Publ. 26. (To appear).

    Google Scholar 

  87. Happel, D.; Rickard, J.; Schofield, A.: Piecewise hereditary algebras. Bull. London Math. Soc. 20 (1988), 23–28.

    Article  MathSciNet  MATH  Google Scholar 

  88. Happel, D.; Ringel, C.M.: The derived category of a tubular algebra. In: Representation Theory I. Springer LNM 1177 (1986). 156–180.

    Google Scholar 

  89. Happel, D.; Unger, L.: Factors of concealed algebras. Math. Z. 201 (1989), 477–483.

    Article  MathSciNet  MATH  Google Scholar 

  90. Happel, D.; Unger, L.: A family of infinite-dimensional non-selfextending bricks for wild hereditary algebras. Proc. Tsukuba Conf. 1990 (To appear).

    Google Scholar 

  91. Hille, L.: Assoziative gestufte Algebren und Kippfolgen mit dim(X)+l Stufen auf projektiven glatten algebraischen Mannigfaltigkeiten. Diplomarbeit Humboldt Univ. Berlin (1990).

    Google Scholar 

  92. Hoshino, M.; Miyachi, J.: Tame triangular matrix algebras over self-injective algebras. Tsukuba J. Math. 11 (1987), 383–391.

    MathSciNet  MATH  Google Scholar 

  93. v. Höhne; H. J.: On weakly positive unit forms. Comm. Math. Helv. 63 (1988), 312–336.

    Article  MATH  Google Scholar 

  94. Hübner, T.: (In preparation).

    Google Scholar 

  95. Igusa, K.: Notes on the loop conjecture. J. Pure and Appl. Algebra. (To appear).

    Google Scholar 

  96. Igusa, K.; Smalø, S.; Todorov, G.: Finite projectivity and contravariant finiteness. (To appear).

    Google Scholar 

  97. Igusa, K.; Todorov, G.: A numerical characterization of finite Auslander-Reiten quivers. In: Representation Theory I. Springer LNM 1177 (1986), 181–198.

    Google Scholar 

  98. Igusa, K.; Zacharia, D.: Syzygy pairs in a monomial algebra. Proc. Amer. Math. Soc. 108 (1990) 601–604.

    Article  MathSciNet  MATH  Google Scholar 

  99. Irving, R.: BGG algebras and the BGG reciprocity principle. J. Algebra 135 (1990), 363–380.

    Article  MathSciNet  MATH  Google Scholar 

  100. Kac, V. G.: Root systems, representations of quivers and invariant theory. In: Invariant Theory. Springer LNM 996 (1983), 74–108.

    Chapter  Google Scholar 

  101. Kapranov, M.M.: On the derived categories of coherent sheaves on some homogeneous spaces. Inv. Math. 92 (1988), 479–508.

    Article  MathSciNet  MATH  Google Scholar 

  102. Keller, B.: Chain complexes and stable categories. Manuscr. Math. 67 (1990), 379–417.

    Article  MATH  Google Scholar 

  103. Keller, B.; Vossieck, D: Sous les catégories dérivées. C.R. Acad. Sci. Paris I 305 (1987) 225–228.

    MathSciNet  MATH  Google Scholar 

  104. Kerner, O.: Preprojective components of wild hereditary algebras. Manuscr. Math. 61 (1988), 429–445.

    Article  MathSciNet  MATH  Google Scholar 

  105. Kerner, O.: Tilting wild algebras. J. London Math. Soc. (2) 39 (1989), 29–47.

    Article  MathSciNet  MATH  Google Scholar 

  106. Kerner, O.: Universal exact sequences for torsion theories. In: Topics in Algebra. Banach Center Publ. 26. (To appear).

    Google Scholar 

  107. Kerner, O.: Stable components of wild tilted algebras. J. Algebra (To appear).

    Google Scholar 

  108. Kerner, O.; Skowronski, A.: On module categories with nilpotent infinite radical. (To appear).

    Google Scholar 

  109. Kirkman, E.; Kuzmanovich, J.: Algebras with large homological dimension. (To appear)

    Google Scholar 

  110. Klemp, B.; Simson, D.: Schurian sp-representation-finite right peak PI-rings and their indecomposable socle projective modules. J. Algebra 134 (1990), 390–468.

    Article  MathSciNet  MATH  Google Scholar 

  111. König, S.: Tilting complexes, perpendicular categories, and recollement of derived module categories of rings. (To appear)

    Google Scholar 

  112. Krause, H.: Maps between tree and band modules. J. Algebra (To appear).

    Google Scholar 

  113. Krause, H.: Endomorphismem von Worten in einem Köcher. Dissertation. Bielefeld 1991.

    Google Scholar 

  114. Le Bruyn, L.: Counterexamples to the Kac-conjecture on Schur roots. Bull. Sci. Math. 110 (1986), 437–448.

    MathSciNet  MATH  Google Scholar 

  115. Lenzing, H.: Nilpotente Elemente in Ringen von endlicher globaler Dimension. Math. Z. 108 (1969), 313–324.

    Article  MathSciNet  MATH  Google Scholar 

  116. Lenzing, H.: Curve singularities arising from the representation theory of tame hereditary Artin algebras. In: Representation Theory I. Springer LNM 1177 (1986), 199–231.

    Google Scholar 

  117. Lenzing, H.: Canonical algebras and rings of automorphic forms. (In preparation).

    Google Scholar 

  118. Lenzing, H.; de la Peña, J. A.: The Auslander-Reiten components of a canonical algebra. (In preparation).

    Google Scholar 

  119. Lusztig, G.: Canonical bases arising from quantized enveloping algebras. J. Amer. Math. Soc. 3 (1990), 447–498

    Article  MathSciNet  MATH  Google Scholar 

  120. Marmaridis, N.; de la Peña, J.A.: Quadratic forms and preinjective modules. J. Algebra 134 (1990), 326–343.

    Article  MATH  Google Scholar 

  121. Marmolejo, E.; Ringel, C.M.: Modules of bounded length in Auslander-Reiten components, Arch. Math. 50 (1988), 128–133.

    Article  MathSciNet  MATH  Google Scholar 

  122. Martínez-Villa, R.: The stable equivalence for algebras of finite representation type. Comm. Algebra 13 (1985), 991–1018.

    Article  MathSciNet  MATH  Google Scholar 

  123. Martínez-Villa, R.: Some remarks on stably equivalent algebras. Comm. Algebra (To appear).

    Google Scholar 

  124. Meltzer, H.: Tilting bundles, repetitive algebras, and derived categories of coherent sheaves. Preprint 193 Humboldt-Universität Berlin (1988)

    Google Scholar 

  125. Menini, C.; Orsatti, A.: Representable equivalences between categories of modules and applications. Rend. Sem. Mat. Univ. Padova 82 (1989), 203–231.

    MathSciNet  MATH  Google Scholar 

  126. Mirollo, R.; Vilonen, K.: Bernstein-Gelfand-Gelfand reciprocity on perverse sheaves. Ann. Sci. E.N.S. 20 (1987), 311–324.

    MathSciNet  MATH  Google Scholar 

  127. Miyashita, Y.: Tilting modules of finite projective dimension. Math. Z. 193 (1986), 113–146.

    Article  MathSciNet  MATH  Google Scholar 

  128. Nazarova, L.A.; Rojter, A.V.: Representations of completed partially ordered sets. In: Proc. Fourth Intern. Conf. Representations of Algebras. Vol.1. Carleton-Ottawa LNS 1 (1985).

    Google Scholar 

  129. Nazarova, L.A.; Rojter, A.V.: Representations of bipartite completed posets. Comment. Math. Helv. 63 (1988), 498–526.

    Article  MathSciNet  MATH  Google Scholar 

  130. Nehring, J.; Skowroński, A.: Polynomial growth trivial extensions of simply connected algebras. Fund. Math. 132 (1989), 117–134.

    MathSciNet  MATH  Google Scholar 

  131. Okuyama, T.: On the Auslander-Reiten quiver of a finite group. J. Algebra 110 (1987), 425–430.

    Article  MathSciNet  MATH  Google Scholar 

  132. Ostermann, A.; Pott, A.: Schwach positive ganze quadratische Formen, die eine aufrichtige, positive Wurzel mit einem Koeffizienten 6 besitzen. J. Algebra 126 (1989), 80–118.

    Article  MathSciNet  MATH  Google Scholar 

  133. Parshall, B.: Finite dimensional algebras and algebraic groups. In: Classical Groups and Related Topics. Contemp. Math. 82 (1989).

    Google Scholar 

  134. Parshall, B; Scott, L.L.: Derived Categories, Quasi-hereditary Algebras, and Algebraic Groups. Proc. Ottawa-Moosonee Workshop Algebra. Carleton-Ottawa Math. LNS 3 (1988), 1–105

    Google Scholar 

  135. Partharasarathy, R.: t-structures dans la catégorie dérivée associée aux représentations d’un carquois. C.R. Acad. Sci. Paris I 304 (1987), 355–357.

    Google Scholar 

  136. de la Peña, J.: On omnipresent modules in simply connected algebras. J. London Math. Soc. (2) 36 (1987), 385–392.

    Article  MathSciNet  MATH  Google Scholar 

  137. de la Peña, J.: Quadratic forms and the representation type of an algebra. Ergänzungsreihe 90-003 SFB 343 Bielefeld.

    Google Scholar 

  138. de la Peña, J.: Tame algebras with sincere directing modules. (To appear).

    Google Scholar 

  139. de la Peña, J., Simson, D.: Prinjective modules, reflection functors, quadratic forms and Auslander-Reiten sequences. (To appear).

    Google Scholar 

  140. de la Peña, J.; Takane, M.: Spectral properties of Coxeter transformations and applications. Arch. Math. 55 (1990), 120–134.

    Article  MATH  Google Scholar 

  141. de la Peña, J.; Tomé, B.: Iterated tubular algebras. J. Pure Appl. Algbera (To appear).

    Google Scholar 

  142. Rickard, J.: Morita theory for derived categories. J. London Math. Soc. 39 (1989), 436–456

    Article  MathSciNet  MATH  Google Scholar 

  143. Rickard, J.: Derived categories and stable equivalence. J. Pure Appl. Algebra 61 (1989), 436–456.

    Article  MathSciNet  Google Scholar 

  144. Rickard, J.: Derived equivalences as derived functors. (To appear).

    Google Scholar 

  145. Rickard, J.; Schofield, A.: Cocovers and tilting modules. Proc. Cambridge Phil. Soc. 106 (1989) 1–5.

    Article  MathSciNet  MATH  Google Scholar 

  146. Riedtmann, Ch.; Schofield, A.: On a simplicial complex associated with tilting modules. Prépubl. l’Inst. Fourier. 137 Grenoble (1989)

    Google Scholar 

  147. Ringel, C.M.: Tame Algebras and Integral Quadratic Forms. Springer LNM 1099 (1984).

    MATH  Google Scholar 

  148. Ringel, C.M.: The regular components of the Auslander-Reiten quiver of a tilted algebra. Chinese Ann. Math. B9 (1988), 1–18.

    MathSciNet  Google Scholar 

  149. Ringel, C.M.: The canonical algebras. (With an appendix by W. Crawley-Boevey). In: Topics in Algebra. Banach Center Publ. 26. (To appear).

    Google Scholar 

  150. Ringel, C.M.: The category of modules with good filtrat ions over a quasi-hereditary algebra has almost split sequences. Math. Z. (To appear).

    Google Scholar 

  151. Ringel, C.M.: On contravariantly finite subcategories. In: Proc. Tsukuba Conf. 1990 (To appear)

    Google Scholar 

  152. Ringel, C.M.: The category of good modules over a quasi-hereditary algebra. In: Proc. Tsukuba Conf. 1990 (To appear)

    Google Scholar 

  153. Ringel, C.M.: Hall algebras. In: Topics in Algebra. Banach Centre Publ. 26. Warszawa (To appear).

    Google Scholar 

  154. Ringel, C.M.: Hall polynomials for the representation-finite hereditary algebras. Adv. Math. 84 (1990), 137–178.

    Article  MathSciNet  MATH  Google Scholar 

  155. Ringel, C.M.: From representations of quivers via Hall and Loewy algebras to quantum groups. In: Proc. Novosibirsk Conf. Algebra 1989 (To appear)

    Google Scholar 

  156. Ringel, C.M.: Hall algebras and quantum groups. Invent. Math. 101 (1990), 583–592

    Article  MathSciNet  MATH  Google Scholar 

  157. Ringel, C.M.: The composition algebra of a cyclic quiver. (To appear)

    Google Scholar 

  158. Ringel, C.M.; Vossieck, D.: Hammocks. Proc. London Math. Soc. (3) 54 (1987), 216–246.

    Article  MathSciNet  MATH  Google Scholar 

  159. Rudakov, A. N. et. al.: Helices and Vector Bundles. Seminaire Rudakov. London Math. Soc. LNS 148 (1990).

    Book  MATH  Google Scholar 

  160. Scheuer, T.: More hammocks. In: Topics in Algebra. Banach Centre Publ. 26. Warszawa (To appear).

    Google Scholar 

  161. Scheuer, T.: The canonical decomposition of the poset of a hammock. Proc. London Math. Soc. (To appear).

    Google Scholar 

  162. Schewe, W.: The set of Z-coverings for a finite translation quiver. Dissertation Bielefeld 1989.

    Google Scholar 

  163. Schewe, W.: Fundamental domains for representation-finite algebras. Rapport 74 Univ. Sherbrooke (1990).

    Google Scholar 

  164. Schofield, A.: Bounding the global dimension in terms of the dimension. Bull. London Math. Soc. 17 (1985), 393–394.

    Article  MathSciNet  MATH  Google Scholar 

  165. Schofield, A.: The field of definition of a real representation of a quiver Q. (To appear)

    Google Scholar 

  166. Schofield, A.: The internal structure of real Schur representations. (To appear)

    Google Scholar 

  167. Schofield, A.: (To appear).

    Google Scholar 

  168. Scott, L.L.: Simulating algebraic geometry with algebra I: The algebraic theory of derived categories. Proc. Symp. Pure Math. 47 (1987), 271–281.

    Google Scholar 

  169. Simson, D.: Module categories and adjusted modules over traced rings. Diss. Math. 269 (1990).

    Google Scholar 

  170. Skowroński, A.: Group algebras of polynomial growth. Manuscr. Math. 59 (1987), 499–516.

    Article  MATH  Google Scholar 

  171. Skowroński, A.: Selfinjective algebras of polynomial growth. Math. Ann. 285 (1989), 177–199.

    Article  MathSciNet  MATH  Google Scholar 

  172. Skowroński, A.: Algebras of polynomial growth. Topics in Algebra. Banach centre publ. 26. (To appear).

    Google Scholar 

  173. Skowroński, A.; Smalø, S.O.: Directing modules. Preprint 8/1990 Univ. Trondheim.

    Google Scholar 

  174. Smalø, S.O.: Functorial finite subcategories over triangular matrix rings. Preprint 6/1989 Trondheim.

    Google Scholar 

  175. Soergel, W.: Kategorie O, perverse Garben und Moduln über den Koinvarianten zur Weylgruppe. J. Amer. Math. Soc. 3 (1990), 421–445.

    MathSciNet  MATH  Google Scholar 

  176. Soergel, W.: Parabolisch-singuläre Dualität für Kategorie O. Preprint MPI Bonn 89–68.

    Google Scholar 

  177. Soergel, W.: Construction of projectives and reciprocity in an abstract setting. (To appear).

    Google Scholar 

  178. Strauß, H.: Tilting modules over wild hereditary algebras. Thesis. Carleton University 1986. Abstract: C.R. Math., Acad. Sci. Canada 9 (1987), 161–166.

    MATH  Google Scholar 

  179. Tachikawa, H., Wakamatsu, T.: Cartan matrices and Grothendieck groups of stable categories. (To appear).

    Google Scholar 

  180. Uematsu, M.; Yamagata, K.: On serial quasi-hereditary rings. Hokkaido Math. J. 19 (1990), 165–174.

    MathSciNet  MATH  Google Scholar 

  181. Unger, L.: Lower bounds for indecomposable, faithful, preinjective modules. Manuscr. Math. 57 (1986), 1–31.

    Article  MathSciNet  MATH  Google Scholar 

  182. Unger, L.: The concealed algebras of the minimal wild hereditary algebras. Bayreuther Math. Schriften 31 (1990), 145–154.

    MathSciNet  MATH  Google Scholar 

  183. Unger, L.: On wild tilted algebras which are squids. Archiv Mathematik (To appear).

    Google Scholar 

  184. Unger, L.: Schur modules over wild, finite dimensional path algebras with three non isomorphic simple modules. J. Pure Appl. Algebra. (To appear).

    Google Scholar 

  185. Unger, L.: On the number of maximal sincere modules over sincere directed algebras. J. Algebra 133 (1990), 211–231.

    Article  MathSciNet  MATH  Google Scholar 

  186. Unger, L.: One-dimensional links of the simplicial complex of partial tilting modules. (In preparation).

    Google Scholar 

  187. Wakamatsu, T.: On modules with trivial selfextensions. J. Algebra 114 (1988), 106–114.

    Article  MathSciNet  MATH  Google Scholar 

  188. Wakamatsu, T.: Stable equivalences for selfinjective algebras and a generalization of tilting modules. J. Algebra 134 (1990), 298–325.

    Article  MathSciNet  MATH  Google Scholar 

  189. Wiedemann, A.: Quotients of quasi-hereditary algebras. (To appear).

    Google Scholar 

  190. Xi, Ch.: Die Vektorraumkategorie zu einem unzerlegbaren projektiven Modul einer Algebra. J. Algebra (To appear).

    Google Scholar 

  191. Xi, Ch.: Die Vektorraumkategorie zu einem Punkt einer zahmen verkleideten Algebra. J. Algebra (To appear).

    Google Scholar 

  192. Xi, Ch.: Die Vektorraumkategorie zu einem unzerlegbaren projektiven Modul einer tubularen Algebra. Manuscr. Math. 69 (1990), 223–235.

    Article  MATH  Google Scholar 

  193. Xi, Ch.: On wild hereditary algebras with small growth numbers. Comm. Algebra 18 (1990), 3413–3422.

    Article  MathSciNet  MATH  Google Scholar 

  194. Xi, Ch.: Minimal elements of the poset of a hammock. Preprint 90-016 SFB 343 Bielefeld.

    Google Scholar 

  195. Xi, Ch.: Quasi-heredity of algebras and their factor algebras. Preprint 90-59 SFB 343 Bielefeld.

    Google Scholar 

  196. Xi, Ch.: Symmetric algebras as endomorphism rings of large projective modules over quasi-hereditary algebras. Preprint 90-59 SFB 343 Bielefeld.

    Google Scholar 

  197. Zavadskij, A. G.: Classification of representations of posets of finite growth. in: Proc. Fourth Intern. Conf. Representations of Algebras. Vol.2. Carleton-Ottawa LNS 2 (1984), 36.01–36.15

    Google Scholar 

  198. Zhang, Y.: The modules in any component of the AR-quivaer of a wild hereditary artin algebra are uniquely determined by their composition factors. Archiv Math. 53 (1989), 250–251.

    Article  MATH  Google Scholar 

  199. Zhang, Y.: Eigenvalues of Coxeter transformations and the structure of the regular components of the Auslander-Reiten quiver. Comm. Algebra. 17 (1989), 2347–2362.

    Article  MathSciNet  MATH  Google Scholar 

  200. Zhang, Y.: The structure of stable components. Can. J. Math. (To appear).

    Google Scholar 

  201. Zimmermann-Huisgen, B.: Bounds on finitistic and global dimension for artinian rings with vanishing radical cube. (To appear).

    Google Scholar 

  202. Zimmermann-Huisgen, B.: Predicting syzygies over monomial algebras. (To appear).

    Google Scholar 

Older surveys

  1. Auslander, M.: The what, where and why of almost split sequences. Proc. Intern. Congr. Math. 1986. Amer. Math. Soc. (1987), Vol.1, 338–345.

    MathSciNet  Google Scholar 

  2. Gabriel, P.: Darstellungen endlichdimensionaler Algebren Proc. Intern. Congr. Math. 1986. Amer. Math. Soc. (1987), Vol.1, 378–388.

    MathSciNet  Google Scholar 

  3. Reiten, I.: An introduction to the representation theory of Artin algebras. Bull. London Math. Soc. 17 (1985), 209–233.

    Article  MathSciNet  MATH  Google Scholar 

  4. Reiten, I.: Finite dimensional algebras and singularities. In: Singularities, Representations of Algebras, and Vector Bundles. Springer LNM 1273 (1987), 35–57.

    Chapter  Google Scholar 

  5. Riedtmann, Ch.: Algèbre de type de représentation fini. Séminaire Bour-baki. 37e année 1984–1985, n. 650. Astérisque 133–134 (1986), 335–350.

    MathSciNet  Google Scholar 

  6. Ringel, C.M.: The representation type of local algebras. In: Representations of Algebras. Springer LNM 488 (1975), 282–305.

    Chapter  Google Scholar 

  7. Ringel, C.M.: Report on the Brauer-Thrall conjectures. In: Representation Theory I. Springer LNM 831 (1980), 104–136

    Chapter  Google Scholar 

  8. Ringel, C.M.: Tame algebras. In: Representation Theory I. Springer LNM 831 (1980), 137–287

    Chapter  Google Scholar 

  9. Ringel, C.M.: Indecomposable representations of finite dimensional algebras. Proceedings Intern. Conf. Math. Warszawa 1983, (1984), 425–436.

    Google Scholar 

  10. Ringel, C.M.: Representation theory of finite dimensional algebras. Durham Lectures 1985. London Math. Soc. Lecture Note Series 116 (1986), 7–79.

    MathSciNet  Google Scholar 

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  1. Claus Michael Ringel
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  1. Institut für Experimentelle Mathematik, Universität GHS Essen, Ellernstrasse 29, D-4300, Essen 12, Germany

    G. O. Michler

  2. Fakultät für Mathematik, Universität Bielefeld, Universitätsstrasse, D-4800, Bielefeld, Germany

    C. M. Ringel

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Ringel, C.M. (1991). Recent Advances in the Representation Theory of Finite Dimensional Algebras. In: Michler, G.O., Ringel, C.M. (eds) Representation Theory of Finite Groups and Finite-Dimensional Algebras. Progress in Mathematics, vol 95. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8658-1_6

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