Skip to main content
SpringerLink
Log in

Geometric methods in representation theory

  • Conference paper
  • First Online:
Representations of Algebras

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 944))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Borho, W., Kraft, H.: Ueber Bahnen und deren Deformationen bei linearen Aktionen reduktiver Gruppen. Comment. Math. Helv. 54 (1979), 61–104

    Article  MathSciNet  MATH  Google Scholar 

  2. Hesselink, W.: Singularities in the nilpotent scheme of a classical group. Trans. Amer. Math. Soc. 222 (1976), 1–32

    Article  MathSciNet  MATH  Google Scholar 

  3. Kraft, H.: Parametrisierung von Konjugationsklassen in sln. Math. Ann. 234 (1978), 209–220.

    Article  MathSciNet  MATH  Google Scholar 

  4. Kraft, H., Procesi, C.: Closures of Conjugacy Classes of Matrices are Normal. Invent. math. 53 (1979), 227–247

    Article  MathSciNet  MATH  Google Scholar 

  5. Peterson, D.: Geometry of the adjoint representation of a complex semisimple Lie algebra. Thesis Harvard University (1978)

    Google Scholar 

  6. Peterson, D.: Affine Cross-Sections for gl/GL. Harvard University, Cambridge, Mass.

    Google Scholar 

  7. Procesi, C., Kraft, H.: Classi coniugate in GL(n, ℂ). Rend. Sem. Mat. Univ. Padova 59 (1978), 209–222.

    MathSciNet  MATH  Google Scholar 

References

  1. Gelfand; I.M. and Ponomarëv V.A.: Non decomposable representations of the Lorentz group, Usp. Mat. Nauk. 23 (1968), 3–60

    Google Scholar 

  2. Luna, D.: Slices étales. Bull. Soc. math. France, Mémoire 33 (1973), 81–105

    MATH  Google Scholar 

  3. Procesi, C.: Finite dimensional representations of algebras. Israel J. Math. 19(1974), 169–182

    Article  MathSciNet  MATH  Google Scholar 

  4. Procesi, C.: The invariant theory of n×n matrices. Adv. math. 19(1976), 306–381

    Article  MathSciNet  MATH  Google Scholar 

  5. Richardson, R.W.: Commuting varieties of semisimple Lie algebras and algebraic groups. compositio Math. 38 (1979), 311–327.

    MathSciNet  MATH  Google Scholar 

References

  1. Hazewinkel, M.: A partial survey of the uses of algebraic geometry in system and control theory. Sym. Math. INDAM (Severi Centennial Conference, 1979), Academic Press

    Google Scholar 

  2. Tannenbaum, A.: Invariance and System Theory: Algebraic and Geometric Aspects. Lecture Notes in Math. 845 (1981), Springer-Verlag

    Google Scholar 

References for chapter II

  1. Birkes, D.: Orbits of linear algebraic groups. Ann Math. 93 (1971), 459–475

    Article  MathSciNet  MATH  Google Scholar 

  2. Borho, W., Kraft, H.: Ueber Bahnen und deren Deformationnen bei linearen Aktionen reduktiver Gruppen. Comment. Math. 54 (1979), 61–104

    Article  MathSciNet  MATH  Google Scholar 

  3. Fogarty, J.: Invariant Theory. W. A. Benjamin, Inc., New York, Amsterdam (1968)

    MATH  Google Scholar 

  4. Gabriel, P.: Finite representation type is open. In: Representations of Algebras. Proceedings of the International Conference, Ottawa 1974. Springer LN 488 (1975), 132–155

    Google Scholar 

  5. Hesselink, W.: Desingularizations of Varieties of Nullforms. Invent. Math. 55 (1979), 141–163

    Article  MathSciNet  MATH  Google Scholar 

  6. Kempf, G.: Instability in Invariant Theory. Ann. Math. 108 (1978), 299–316

    Article  MathSciNet  MATH  Google Scholar 

  7. Kraft, H.: Geometrische Methoden in der Invariantentheorie. Vieweg-Verlag (forthcoming)

    Google Scholar 

  8. Luna, D.: Slices étales. Bull. Soc. Math. France, Mémoires 33 (1973), 81–105

    MATH  Google Scholar 

  9. Mazzola, G.: The algebraic and geometric classification of associative algebras of dimension five. Manuscripta Math. 27 (1979), 81–101

    Article  MathSciNet  MATH  Google Scholar 

  10. Mazzola, G.: Generic finite schemes and Hochschild cocycles. Comment. Math. Helv. 55 (1980), 267–293

    Article  MathSciNet  MATH  Google Scholar 

  11. Mumford, D.: Geometric Invariant Theory. Erg. d. Math. 34 (1970). Springer-Verlag: Berlin-Heidelberg-New York

    MATH  Google Scholar 

  12. Procesi, C.: Finite dimensional representations of algebras. Israel J. Math. 19 (1974), 169–182

    Article  MathSciNet  MATH  Google Scholar 

  13. Springer, T. A.: Invariant Theory. Springer LN 585 (1977)

    Google Scholar 

References for chapter III

  1. Auslander, M.: Representation theory of artin algebras II. Comm. Algebra 1 (1974), 269–310

    Article  MathSciNet  MATH  Google Scholar 

  2. Gabriel, P.: Finite representation type is open. In: Representations of Algebras. Proceedings of the International Conference, Ottawa 1974. Springer LN 488 (1975), 132–155

    Google Scholar 

  3. Nazarova, L.A.; Roiter, A.V.: Categorical matricial problems and the conjecture of Brauer-Thrall (Russian) preprint, Inst. Math. Acad. Sci., Kiev 1973, German translation in Mitt. Math. Sem. Giessen 115 (1975)

    Google Scholar 

References

  1. Auslander, M.: Representation theory of artin algebras II. Comm. Algebra 1 (1974), 269–310

    Article  MathSciNet  MATH  Google Scholar 

  2. Birkes, D.: Orbits of linear algebraic groups. Ann. Math. 93 (1971), 459–475

    Article  MathSciNet  MATH  Google Scholar 

  3. Borho, W., Kraft, H.: Ueber Bahnen und deren Deformationen bei linearen Aktionen reduktiver Gruppen. Comment. Math. 54. (1979), 61–104

    Article  MathSciNet  MATH  Google Scholar 

  4. Fogarty, J.: Invariant Theory. W. A. Benjamin, Inc., New York, Amsterdam (1968)

    MATH  Google Scholar 

  5. Gabriel, P.: Finite representation type is open. In: Representations of Algebras. Proceedings of the International Conference, Ottawa 1974. Springer LN 488 (1975), 132–155

    Google Scholar 

  6. Gelfand, I. M. and Ponomarëv V. A.: Non decomposable representations of the Lorentz group, Usp. Mat. Nauk. 23 (1968), 3–60

    Google Scholar 

  7. Hazewinkel, M.: A partial survey of the uses of algebraic geometry in system and control theory. Sym. Math. INDAM (Severi Centennial Conference, 1979), Academic Press

    Google Scholar 

  8. Hesselink, W.: singularities in the nilpotent scheme of a classical group. Trans. Amer. Math. Soc. 222 (1976), 1–32

    Article  MathSciNet  MATH  Google Scholar 

  9. Hesselink, W.: Desingularizations of Varieties of Nullforms. Invent. Math. 55 (1979), 141–163

    Article  MathSciNet  MATH  Google Scholar 

  10. Kempf, G. Instability in Invariant Theory. Ann. Math. 108 (1978). 299–316

    Article  MathSciNet  MATH  Google Scholar 

  11. Kraft, H.: Parametrisierung von Konjugationsklassen in sln. Math. Ann. 234 (1978), 209–220

    Article  MathSciNet  MATH  Google Scholar 

  12. Kraft, H.: Geometrische Methoden in der Invariantentheorie. Vieweg-Verlag (forthcoming)

    Google Scholar 

  13. Kraft, H., Procesi, C.: Closures of Conjugacy Classes of Matrices are Normal. Invent. math. 53 (1979), 227–247

    Article  MathSciNet  MATH  Google Scholar 

  14. Luna, D.: Slices étales. Bull. Soc. Math. France, Mémoires 33 (1973), 81–105

    MATH  Google Scholar 

  15. Mazzola, G.: The algebraic and geometric classification of associative algebras of dimension five. Manuscripta Math. 27 (1979), 81–101

    Article  MathSciNet  MATH  Google Scholar 

  16. Mazzola, G.: Generic finite schemes and Hochschild cocycles. Comment. Math. Helv. 55 (1980), 267–293

    Article  MathSciNet  MATH  Google Scholar 

  17. Mumford, D.: Geometric Invariant Theory. Erg. d. Math. 34 (1970). Springer-Verlag: Berlin-Heidelberg-New York

    MATH  Google Scholar 

  18. Nazarova, L. A., Roiter, A. V.: Catgorical matricial problems and the conjecture of Brauer-Thrall (Russian) preprint, Inst. Math. Acad. Sci., Kiev 1973, German translation in Mitt. Math. Sem. Giessen 115 (1975)

    Google Scholar 

  19. Peterson, D.: Geometry of the adjoint representation of a complex semisimple Lie algebra. Thesis Harvard University (1978)

    Google Scholar 

  20. Peterson, D.: Affine Cross-Sections for gl/GL. Harvard University, Cambridge, Mass.

    Google Scholar 

  21. Procesi, C.: Finite dimensional representations of algebras. Israel J. Math. 19 (1974), 169–182

    Article  MathSciNet  MATH  Google Scholar 

  22. Procesi, C.: The Invariant Theory of nxn matrices. 19 (1976), 306–381

    MathSciNet  Google Scholar 

  23. Procesi C., Kraft, H.: Classi coniugate in GL (n, ℂ). Rend. Sem. Mat. Univ. Padova 59 (1978), 209–222

    MathSciNet  MATH  Google Scholar 

  24. Richardson, R. W.: Commuting varieties of semisimple Lie algebras and algebraic groups. Composition Math. 38 (1979), 311–327

    MathSciNet  MATH  Google Scholar 

  25. Springer, T. A.: Invariant Theory. Springer LN 585 (1977)

    Google Scholar 

  26. Tannenbaum, A.: Invariance and System Theory: Algebraic and Geometric Aspects. Lecture Notes in Math. 845 (1981), Springer-Verlag

    Google Scholar 

Download references

Authors
  1. Hanspeter Kraft
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Maurice Auslander Emilio Lluis

Rights and permissions

Reprints and permissions

Copyright information

© 1982 Springer-Verlag

About this paper

Cite this paper

Kraft, H. (1982). Geometric methods in representation theory. In: Auslander, M., Lluis, E. (eds) Representations of Algebras. Lecture Notes in Mathematics, vol 944. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0094059

Download citation

  • DOI: https://doi.org/10.1007/BFb0094059

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11577-9

  • Online ISBN: 978-3-540-39313-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation