Character clusters for Lie algebra modules over a field of non-zero characteristic

Abstract

For a Lie algebra L over an algebraically closed field of non-zero characteristic, every finite-dimensional L-module can be decomposed into a direct sum of submodules such that all composition factors of a summand have the same character. Using the concept of a character cluster, this result is generalised to fields which are not algebraically closed. Clusters are used to generalise the construction of induced modules.

8 pages

Cited by in corpus (3)

• Induced modules for modular Lie algebras
• Blocks of representations of Lie algebras
• On $\mathfrak{F}$-hypercentral modules and character clusters