Skip to main content
Log in

On the vanishing of extensions of modules over reduced enveloping algebras

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. H.H. Andersen, Extensions of modules for algebraic groups, Amer. J. Math.106 (1984), 498–504

    Google Scholar 

  2. D.J. Benson, J.F. Carlson, Complexity and Multiple Complexes, Math. Z.195 (1987), 221–238

    Google Scholar 

  3. D.J. Benson, J.F. Carlson, G.R. Robinson, On the Vanishing of Group Cohomology, J. Algebra131 (1990), 40–73

    Google Scholar 

  4. R.E. Block, R.L. Wilson, Classification of restricted simple Lie algebras, J. Algebra114 (1988), 115–259

    Google Scholar 

  5. J.F. Carlson, The varieties and cohomology ring of a module, J. Algebra85 (1983), 104–143

    Google Scholar 

  6. J.F. Carlson, Module varieties and cohomology rings of finite groups, Vorlesungen aus dem Fachbereich Mathematick der Universität Essen, 1985

  7. J.F. Carlson, Varieties for modules, Proc. of Sym. in Pure Math.47 (1987), 37–44

    Google Scholar 

  8. J. Feldvoss, On the cohomology of restricted Lie algebras, Comm. Alg19(10) (1991), 2865–2906

    Google Scholar 

  9. E.M. Friedlander, B.J. Parshall, Support varieties for restricted Lie algebras, Invent. Math.86 (1986), 553–562

    Google Scholar 

  10. E.M. Friedlander, B.J. Parshall, On the cohomology of algebraic and related groups, Inv. Math.74 (1983), 85–117

    Google Scholar 

  11. E.M. Friedlander, B.J. Parshall, Geometry ofp-unipotent Lie algebras, J. Algebra109 (1987), 25–45

    Google Scholar 

  12. E.M. Friedlander, B.J. Parshall, Modular representation theory of Lie algebras, Amer. J. Math.110 (1988), 1055–1094

    Google Scholar 

  13. E.M. Friedlander, B.J. Parshall, Deformations of Lie algebra representations, Amer. J. Math.112 (1990), 375–395

    Google Scholar 

  14. E.M. Friedlander, B.J. Parshall, Induction, deformation, and specialization, Math. Ann.290 (1991), 473–489

    Google Scholar 

  15. G. Hochschild, Cohomology of restricted Lie algebras, Amer. J. Math.76 (1954), 555–580

    Google Scholar 

  16. R.R. Holmes, D.K. Nakano, Brauer-type reciprocity for a class of graded associative algebras, J. Algebra144(1) (1991), 117–125

    Google Scholar 

  17. R.R. Holmes, D.K. Nakano, Block degeneracy and Cartan invariants for graded Lie algebras of Cartan type. J. Algebra161 (1993), 155–170

    Google Scholar 

  18. J.E. Humphreys, Modular representations of classical Lie algebras and semisimple groups, J. Algebra19 (1971), 51–79

    Google Scholar 

  19. J.C. Jantzen, Representations of Algebraic Groups, Academic Press, 1987

  20. V. Kac, B. Weisfeiler, The irreducible representations of Liep-algebras, Functional Anal. Appl.5 (1971), 471–503

    Google Scholar 

  21. V. Kac, B. Weisfeiler, Coadjoint action of a semisimple algebraic group and the center of the enveloping algebra in characteristicp, Indag. Math.38 (1976), 135–151

    Google Scholar 

  22. Z. Lin, D.K. Nakano, Algebraic group techniques in the representation and cohomology theory of Lie algebras of Cartan type. J. Algebra (to appear)

  23. P.A. Linnel, Cohomology of finite soluble groups, J. Algebra107 (1987), 53–62

    Google Scholar 

  24. P.A. Linnel, U. Stammbach, The cohomology ofp-constrained groups, J. Pure Appl. Algebra49 (1987), 273–279

    Google Scholar 

  25. D.K. Nakano, Projective modules over Lie algebras of Cartan type, Memoirs of AMS98 470 (1992)

    Google Scholar 

  26. D.K. Nakano, A bound on the complexity forG r T modules, to appear in Proc. AMS

  27. R.D. Pollack, Restricted Lie algebras of bounded type, Bull. of AMS74(2) (1968), 326–331

    Google Scholar 

  28. Strade, H., Farnsteiner, R.: Modular Lie algebras and their representations, Marcel Dekker, 1988

Download references

Author information

Authors and Affiliations

Authors

Additional information

Supported by NSF grants DMS-9001689 and DMS-9301929

Supported by NSF grant DMS-9206284

Rights and permissions

Reprints and permissions

About this article

Cite this article

Carlson, J.F., Nakano, D.K. & Peters, K.M. On the vanishing of extensions of modules over reduced enveloping algebras. Math. Ann. 302, 541–560 (1995). https://doi.org/10.1007/BF01444507

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01444507

Mathematics Subject Classification (1991)

Navigation