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arXiv · 1405.4600

Blocks of representations of Lie algebras

Donald W. Barnes
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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.

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Donald W. Barnes. 2014-05-19. Blocks of representations of Lie algebras. https://arxiv.org/abs/1405.4600

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