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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Barnes, D.W.: On the cohomology of soluble Lie algebras. Math. Z. 101, 343–349 (1967).
Barnes, D.W.: First cohomology groups of soluble Lie algebras. J. Algebra 46, 292–297 (1977).
Dzumadil’daev, A.S.: On the cohomology of modular Lie algebras. Math. USSR Sbornik 47 (1), 127–143 (1984).
Dzumadil’daev, A.S.: Cohomology of truncated coinduced representations of Lie algebras of positive characteristic. Math. USSR Sbornik 66 (2), 461–473 (1990).
Farnsteiner, R.: On the vanishing of homology and cohomology groups of associative algebras. Trans. Amer. Math. Soc. 306 (2), 651–665 (1988).
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.
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).
Feldvoss, J.: Homologische Aspekte der Darstellungstheorie modularer Lie-Algebren. Dissertation, Universität Hamburg, 1989.
Feldvoss, J.: On the cohomology of restricted Lie algebras. Comm. Algebra 19 (10), 2865–2906 (1991).
Feldvoss, J.: On the block structure of solvable restricted Lie algebras. Submitted.
Fischer, G.: Darstellungstheorie des ersten Frobeniuskerns der SL 2. Dissertation, Universität Bielefeld, 1982.
Hochschild, G.P.: Cohomology of restricted Lie algebras. Amer. J. Math. 76, 555–580 (1954).
Hochschild, G.P.: Representations of restricted Lie algebras of characteristic p. Proc. Amer. Math. Soc. 5, 603–605 (1954).
Stammbach, U.: Cohomological characterisations of finite solvable and nilpotent groups. J. Pure Appl. Algebra 11, 293–301 (1977).
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.
Voigt, D.: Induzierte Darstellungen in der Theorie der endlichen, algebraischen Gruppen. Lecture Notes in Mathematics 592, Springer-Verlag, Berlin-Heidelberg-New York, 1977.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights 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