Split Strongly Abelian p-Chief Factors and First Degree Restricted Cohomology

Authors

Jorg Feldvoss, University of South AlabamaFollow
Salvatore Siciliano, University of Salento, ItalyFollow
Thomas Weigel, University of Milano-Bicocca, ItalyFollow

Document Type

Article

Publication Title

Journal of Lie Theory

Abstract

In this paper we investigate the relation between the multiplicities of split strongly abelian p-chief factors of finite-dimensional restricted Lie algebras and first degree restricted cohomology. As an application we obtain a characterization of solvable restricted Lie algebras in terms of the multiplicities of split strongly abelian p-chief factors. Moreover, we derive some results in the representation theory of restricted Lie algebras related to the principal block and the projective cover of the trivial irreducible module of a finite-dimensional restricted Lie algebra. In particular, we obtain a characterization of finite-dimensional solvable restricted Lie algebras in terms of the second Loewy layer of the projective cover of the trivial irreducible module. The analogues of these results are well known in the modular representation theory of finite groups.

First Page

29

Last Page

39

Publication Date

2014

Department

Mathematics and Statistics

Comments

This is the pre-print version of this article. The published version can be found in the Journal of Lie Theory at this link: https://www.heldermann.de/JLT/JLT24/JLT241/jlt24002.htm

Recommended Citation

Feldvoss, J., Siciliano, S., & Weigel, T. (2013). Split strongly abelian p-chief factors and first degree restricted cohomology. Journal of Lie Theory, 24(1), 29-39.