Mathematische Annalen

, Volume 302, Issue 1, pp 541–560

On the vanishing of extensions of modules over reduced enveloping algebras

  • Jon F. Carlson
  • Daniel K. Nakano
  • Karl M. Peters
Article

Mathematics Subject Classification (1991)

17B55 20G 17B50 

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References

  1. [And]
    H.H. Andersen, Extensions of modules for algebraic groups, Amer. J. Math.106 (1984), 498–504Google Scholar
  2. [BC]
    D.J. Benson, J.F. Carlson, Complexity and Multiple Complexes, Math. Z.195 (1987), 221–238Google Scholar
  3. [BCR]
    D.J. Benson, J.F. Carlson, G.R. Robinson, On the Vanishing of Group Cohomology, J. Algebra131 (1990), 40–73Google Scholar
  4. [BW]
    R.E. Block, R.L. Wilson, Classification of restricted simple Lie algebras, J. Algebra114 (1988), 115–259Google Scholar
  5. [Cal]
    J.F. Carlson, The varieties and cohomology ring of a module, J. Algebra85 (1983), 104–143Google Scholar
  6. [Ca2]
    J.F. Carlson, Module varieties and cohomology rings of finite groups, Vorlesungen aus dem Fachbereich Mathematick der Universität Essen, 1985Google Scholar
  7. [Ca3]
    J.F. Carlson, Varieties for modules, Proc. of Sym. in Pure Math.47 (1987), 37–44Google Scholar
  8. [Feld]
    J. Feldvoss, On the cohomology of restricted Lie algebras, Comm. Alg19(10) (1991), 2865–2906Google Scholar
  9. [FP1]
    E.M. Friedlander, B.J. Parshall, Support varieties for restricted Lie algebras, Invent. Math.86 (1986), 553–562Google Scholar
  10. [FP2]
    E.M. Friedlander, B.J. Parshall, On the cohomology of algebraic and related groups, Inv. Math.74 (1983), 85–117Google Scholar
  11. [FP3]
    E.M. Friedlander, B.J. Parshall, Geometry ofp-unipotent Lie algebras, J. Algebra109 (1987), 25–45Google Scholar
  12. [FP4]
    E.M. Friedlander, B.J. Parshall, Modular representation theory of Lie algebras, Amer. J. Math.110 (1988), 1055–1094Google Scholar
  13. [FP5]
    E.M. Friedlander, B.J. Parshall, Deformations of Lie algebra representations, Amer. J. Math.112 (1990), 375–395Google Scholar
  14. [FP6]
    E.M. Friedlander, B.J. Parshall, Induction, deformation, and specialization, Math. Ann.290 (1991), 473–489Google Scholar
  15. [Ho]
    G. Hochschild, Cohomology of restricted Lie algebras, Amer. J. Math.76 (1954), 555–580Google Scholar
  16. [HolN1]
    R.R. Holmes, D.K. Nakano, Brauer-type reciprocity for a class of graded associative algebras, J. Algebra144(1) (1991), 117–125Google Scholar
  17. [HolN2]
    R.R. Holmes, D.K. Nakano, Block degeneracy and Cartan invariants for graded Lie algebras of Cartan type. J. Algebra161 (1993), 155–170Google Scholar
  18. [Hu]
    J.E. Humphreys, Modular representations of classical Lie algebras and semisimple groups, J. Algebra19 (1971), 51–79Google Scholar
  19. [Jan]
    J.C. Jantzen, Representations of Algebraic Groups, Academic Press, 1987Google Scholar
  20. [KW1]
    V. Kac, B. Weisfeiler, The irreducible representations of Liep-algebras, Functional Anal. Appl.5 (1971), 471–503Google Scholar
  21. [KW2]
    V. Kac, B. Weisfeiler, Coadjoint action of a semisimple algebraic group and the center of the enveloping algebra in characteristicp, Indag. Math.38 (1976), 135–151Google Scholar
  22. [LN]
    Z. Lin, D.K. Nakano, Algebraic group techniques in the representation and cohomology theory of Lie algebras of Cartan type. J. Algebra (to appear)Google Scholar
  23. [L]
    P.A. Linnel, Cohomology of finite soluble groups, J. Algebra107 (1987), 53–62Google Scholar
  24. [LS]
    P.A. Linnel, U. Stammbach, The cohomology ofp-constrained groups, J. Pure Appl. Algebra49 (1987), 273–279Google Scholar
  25. [N1]
    D.K. Nakano, Projective modules over Lie algebras of Cartan type, Memoirs of AMS98 470 (1992)Google Scholar
  26. [N2]
    D.K. Nakano, A bound on the complexity forG r T modules, to appear in Proc. AMSGoogle Scholar
  27. [Po]
    R.D. Pollack, Restricted Lie algebras of bounded type, Bull. of AMS74(2) (1968), 326–331Google Scholar
  28. [SF]
    Strade, H., Farnsteiner, R.: Modular Lie algebras and their representations, Marcel Dekker, 1988Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Jon F. Carlson
    • 1
  • Daniel K. Nakano
    • 2
  • Karl M. Peters
    • 3
  1. 1.Department of MathematicsUniversity of GeorgiaAthensUSA
  2. 2.Department of MathematicsUtah State UniversityLoganUSA
  3. 3.Department of Mathematical SciencesLoyola UniversityChicagoUSA

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