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. © 2014 Heldermann Verlag.

Feldvoss, J., Siciliano, S., Weigel, T. (2014). Split Strongly abelian p-chief factors and first degree restricted cohomology. JOURNAL OF LIE THEORY, 24(1), 29-39.

Split Strongly abelian p-chief factors and first degree restricted cohomology

WEIGEL, THOMAS STEFAN
Ultimo
2014

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. © 2014 Heldermann Verlag.
Articolo in rivista - Articolo scientifico
Irreducible module; Loewy layer; Multiplicity of a split strongly abelian p-chief factor; P-chief factor; Principal block; Projective indecomposable module; Restricted cohomology; Solvable restricted lie algebra; Split p-chief factor; Strongly abelian p-chief factor; Transgression; Algebra and Number Theory
English
2014
24
1
29
39
reserved
Feldvoss, J., Siciliano, S., Weigel, T. (2014). Split Strongly abelian p-chief factors and first degree restricted cohomology. JOURNAL OF LIE THEORY, 24(1), 29-39.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/83699
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