Blocks of representations of Lie algebras
arXiv:1405.4600
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.
arXiv commentThis paper has been withdrawn by the author due to an error in the proof of Lemma 4.22.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