Skip to main content
Log in

Shapiro's lemma and its consequences in the cohomology theory of modular Lie algebras

  • Published:
Mathematische Zeitschrift 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. Berkson, A.J.: Theu-algebra of a restricted Lie algebra is Frobenius. Proc. Am. Math. Soc.15, 14–15 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  2. Cartan, H., Eilenberg, S.: Homological algebra. Princeton: Princeton University Press 1956

    MATH  Google Scholar 

  3. Chang, H.J.: Über Wittsche Lie Ringe. Abh. Math. Semin. Univ. Hamb.14, 151–184 (1941)

    Google Scholar 

  4. Chevalley, C., Eilenberg, S.: Cohomology theory of Lie groups and Lie algebras. Trans. Am. Math. Soc.63, 85–124 (1948)

    Article  MATH  MathSciNet  Google Scholar 

  5. Chwe, B.S.: On the commutativity of restricted Lie algebras. Proc. Am. Math. Soc.16, 547 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  6. Dzhumadil'daev, A.S.: Cohomology of modular Lie algebras. Math. USSR, Sb.47, 127–143 (1984)

    Article  MATH  Google Scholar 

  7. Faith, C., Walker, E.A.: Direct sum decompositions of injective modules. J. Algebra5, 203–221 (1967)

    Article  MATH  MathSciNet  Google Scholar 

  8. Farnsteiner, R.: On ad-semisimple Lie algebras. J. Algebra83, 510–519 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  9. Farnsteiner, R.: Conditions for the commutativity of restricted Lie algebras. Commun. Algebra13, 1475–1489 (1985)

    MATH  MathSciNet  Google Scholar 

  10. Farnsteiner, R.: Central extensions and invariant forms of graded Lie algebras. Algebras Groups Geom.3, 431–455 (1986)

    MATH  MathSciNet  Google Scholar 

  11. Farnsteiner, R.: Dual space derivations andH 2(L, F) of modular Lie algebras. Can. J. Math.39, 1078–1106 (1987)

    MATH  MathSciNet  Google Scholar 

  12. Farnsteiner, R.: On the cohomology of associative algebras and Lie algebras. Proc. Am. Math. Soc.99, 415–420 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  13. Farnsteiner, R.: On the vanishing of homology and cohomology groups of associative algebras. Trans. Am. Math. Soc.306, 651–665 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  14. Farnsteiner, R.: Cohomology groups of infinite dimensional algebras. Math. Z.199, 407–423 (1988)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  17. Hilton, P.J., Stammbach, U.: A course in homological algebra. (Graduate Texts, vol. 4) Berlin Heidelberg New York: Springer 1970

    Google Scholar 

  18. Hochschild, G.P., Serre, J.P.: Cohomology of Lie algebras. Ann. Math.57, 591–603 (1953)

    Article  MathSciNet  Google Scholar 

  19. Hochschild, G.P.: On the cohomology groups of an associative algebra. Ann. Math.46, 58–67 (1945)

    Article  MathSciNet  Google Scholar 

  20. Hochschild, G.P.: Cohomology of restricted Lie algebras. Am. J. Math.76, 555–580 (1954)

    Article  MATH  MathSciNet  Google Scholar 

  21. Humphreys, J.E.: Restricted Lie algebras (and beyond). Contemp. Math.13, 91–98 (1982)

    MATH  MathSciNet  Google Scholar 

  22. Pareigis, B.: Einige Bemerkungen über Frobenius-Erweiterungen. Math. Ann.153, 1–13 (1964)

    Article  MathSciNet  Google Scholar 

  23. Seligman, G.B.: Modular Lie algebras. (Ergeb. Math. Grenzgeb. vol. 40), Berlin Heidelberg New York: Springer 1967

    MATH  Google Scholar 

  24. Sen, C., Shen, G.: Cohomology of graded Lie algebras of Cartan type of characteristic p. Abh. Math. Semin. Univ. Hamb.57, 139–156 (1987)

    Article  MATH  Google Scholar 

  25. Strade, H.: Representations of the Witt algebra. J. Algebra49, 595–605 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  26. Strade, H.: Darstellungen Auflösbarer Lie Algebren. Math. Ann.232, 15–32 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  27. Strade, H., Farnsteiner, R.: Modular Lie algebras and their representations. (Textbooks and Monographs, vol. 116), New York: Dekker 1988

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Farnsteiner, R., Strade, H. Shapiro's lemma and its consequences in the cohomology theory of modular Lie algebras. Math Z 206, 153–168 (1991). https://doi.org/10.1007/BF02571333

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02571333

Keywords

Navigation