Skip to main content

A Cohomological Characterization of Solvable Modular Lie Algebras

  • Chapter
Non-Associative Algebra and Its Applications

Part of the book series: Mathematics and Its Applications ((MAIA,volume 303))

  • 541 Accesses

Abstract

We give a unifying approach to characterizations of some classes of finite dimensional solvable modular Lie algebras by the vanishing of their cohomology and the structure of their principal block.

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

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. Barnes, D.W.: On the cohomology of soluble Lie algebras. Math. Z. 101, 343–349 (1967).

    Article  MathSciNet  MATH  Google Scholar 

  2. Barnes, D.W.: First cohomology groups of soluble Lie algebras. J. Algebra 46, 292–297 (1977).

    Article  MathSciNet  MATH  Google Scholar 

  3. Dzumadil’daev, A.S.: On the cohomology of modular Lie algebras. Math. USSR Sbornik 47 (1), 127–143 (1984).

    Article  Google Scholar 

  4. Dzumadil’daev, A.S.: Cohomology of truncated coinduced representations of Lie algebras of positive characteristic. Math. USSR Sbornik 66 (2), 461–473 (1990).

    Article  Google Scholar 

  5. Farnsteiner, R.: On the vanishing of homology and cohomology groups of associative algebras. Trans. Amer. Math. Soc. 306 (2), 651–665 (1988).

    Article  MathSciNet  MATH  Google Scholar 

  6. Farnsteiner, R.: Recent developments in the cohomology theory of modular Lie algebras. In: International Symposium on Non-.Associative.Algebras and Related Topics, Hiroshima 1990 (eds. K. Yamaguti and N. Kawamoto ), 19–48. World Scientific, Singapore, 1991.

    Google Scholar 

  7. Farnsteiner, R. and Strade, H.: Shapiro’s lemma and its consequences in the cohomology theory of modular Lie algebras. Math. Z. 106, 153–168 (1991).

    Article  MathSciNet  Google Scholar 

  8. Feldvoss, J.: Homologische Aspekte der Darstellungstheorie modularer Lie-Algebren. Dissertation, Universität Hamburg, 1989.

    MATH  Google Scholar 

  9. Feldvoss, J.: On the cohomology of restricted Lie algebras. Comm. Algebra 19 (10), 2865–2906 (1991).

    Article  MathSciNet  MATH  Google Scholar 

  10. Feldvoss, J.: On the block structure of solvable restricted Lie algebras. Submitted.

    Google Scholar 

  11. Fischer, G.: Darstellungstheorie des ersten Frobeniuskerns der SL 2. Dissertation, Universität Bielefeld, 1982.

    MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  13. Hochschild, G.P.: Representations of restricted Lie algebras of characteristic p. Proc. Amer. Math. Soc. 5, 603–605 (1954).

    MathSciNet  MATH  Google Scholar 

  14. Stammbach, U.: Cohomological characterisations of finite solvable and nilpotent groups. J. Pure Appl. Algebra 11, 293–301 (1977).

    Article  MathSciNet  Google Scholar 

  15. Strade, H. and Farnsteiner, R.: Modular Lie Algebras and Their Representations. Monographs and Textbooks in Pure and Applied Mathematics 116, Marcel Dekker, Inc., New York and Basel, 1988.

    MATH  Google Scholar 

  16. Voigt, D.: Induzierte Darstellungen in der Theorie der endlichen, algebraischen Gruppen. Lecture Notes in Mathematics 592, Springer-Verlag, Berlin-Heidelberg-New York, 1977.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Feldvoss, J. (1994). A Cohomological Characterization of Solvable Modular Lie Algebras. In: González, S. (eds) Non-Associative Algebra and Its Applications. Mathematics and Its Applications, vol 303. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0990-1_21

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-0990-1_21

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4429-5

  • Online ISBN: 978-94-011-0990-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics