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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