Document Type

Article

Publication Title

Transformation Groups

Abstract

In this paper it is shown that the projective cover of the trivial irreducible module of a finite-dimensional solvable restricted Lie algebra is induced from the one dimensional trivial module of a maximal torus. As a consequence, the number of the isomorphism classes of irreducible modules with a fixed p-character for a finite-dimensional solvable restricted Lie algebra L is bounded above by p MT(L), where MT(L) denotes the maximal dimension of a torus in L. Finally, it is proved that in characteristic p > 3 the projective cover of the trivial irreducible L-module is induced from the one-dimensional trivial module of a torus of maximal dimension, only if L is solvable.

First Page

377

Last Page

398

DOI

https://doi.org/10.1007/s00031-015-9362-5

Publication Date

2016

Department

Mathematics and Statistics

Comments

This is the pre-print version of this article. The published version can be found at the following link: https://link.springer.com/article/10.1007/s00031-015-9362-5 or https://doi.org/10.1007/s00031-015-9362-5.

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