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Modular Lie representations of finite groups

Published online by Cambridge University Press:  09 April 2009

R. M. Bryant
Affiliation:
School of Mathematics, University of Manchester, PO Box 88, Manchester M60 1QD, England e-mail: roger.bryant@manchester.ac.uk
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Abstract

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Let K be a field of prime characteristic p and let G be a finite group with a Sylow p-subgroup of order p. For any finite-dimensional K G-module V and any positive integer n, let Ln (V) denote the nth homogeneous component of the free Lie K-algebra generated by (a basis of) V. Then Ln(V) can be considered as a K G-module, called the nth Lie power of V. The main result of the paper is a formula which describes the module structure of Ln(V) up to isomorphism.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2004

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