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

2013/01/20 by Donald W. Barnes, Barnes, Donald W. · 2 citations
Mathematics · #17B10 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA) #math.RA #msc:17B10

paper · pdf · doi:10.48550/arxiv.1301.4710

8 pages

arxiv created 2013/01/20 · openalex publication_date 2013/01/20 · arxiv updated 2013/01/22 · openalex created_date 2022/09/17 · openalex updated_date 2026/07/28

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.

Cited by

• Induced modules for modular Lie algebras
• Blocks of representations of Lie algebras

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