Blocks of representations of Lie algebras

2014/05/19 by Donald W. Barnes, Barnes, Donald W.
Mathematics · #17B30 #17B50 #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA) #math.RA #msc:17B30 #msc:17B50

paper · pdf · doi:10.48550/arxiv.1405.4600

This paper has been withdrawn by the author due to an error in the proof of Lemma 4.22. It is possible for the extension to split

openalex publication_date 2014/05/19 · arxiv created 2015/03/11 · arxiv updated 2015/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the theory of finite groups, the irreducible representations of G over a field F are classified into blocks based on a direct decompositions of the group algebra FG. This gives a natural decomposition of FG-modules into direct summands, each summand having all its composition factors belonging to a single block. This block decomposition is the finest natural decomposition of the FG-modules. In this paper, a classification of the irreducible representations of a finite dimensional Lie algebra L into blocks is defined, giving the finest natural direct decomposition of L-modules. This classification is investigated for supersoluble algebras.

Citations

• Induced modules for modular Lie algebras
• Character clusters for Lie algebra modules over a field of non-zero characteristic

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• Classification of quasifinite representations of a Lie algebra related to Block type
• Highest weight representations of a Lie algebra of Block type
• Finite dimensional compact and unitary Lie superalgebras
• The Decomposition of Lie Powers