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Modular Lie representations of finite groups

Part of: Lie algebras and Lie superalgebras Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

R. M. Bryant
R. M. Bryant
Affiliation:
School of Mathematics, University of Manchester, PO Box 88, Manchester M60 1QD, England e-mail: [email protected]
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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.

MSC classification

Secondary: 17B01: Identities, free Lie (super)algebras 20C20: Modular representations and characters
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 77 , Issue 3 , December 2004 , pp. 401 - 424
Copyright
Copyright © Australian Mathematical Society 2004

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