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

Authors

  • D. W. Barnes University of Sydney

Keywords:

Lie algebras, saturated formations, induced modules

Abstract

For a Lie algebra L over an algebraically closed field F 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 resuilt is generalised to fields which are not algebraically closed. Also, it is shown that if the soluble Lie algebra L is in the saturated formation \F and if V, W are irreducible L-modules with the same cluster and the p-operation vanishes on the centre of the p-envelope used, then V,W\) are either both \F-central or both \F-eccentric. Clusters are used to generalise the construction of induced modules. 10.1017/S0004972713000312

Author Biography

D. W. Barnes, University of Sydney

School of Mathematics and Statistics Honorary Associate

Published

2014-01-27

Issue

Vol. 89 No. 2 (2014)

Section

Articles
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