Bryant, R. M. and Stöhr, Ralph
(2005)
*Lie powers in prime degree.*
The Quarterly Journal of Mathematics, 56 (4).
pp. 473-489.
ISSN 0033-5606

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Official URL: http://qjmath.oxfordjournals.org/

## Abstract

Let Lp(V) denote the pth Lie power of a finite-dimensional module V for a group G over a field of prime characteristic p, where Lp(V) is regarded as a submodule of the tensor power Tp(V). There is a natural homomorphism from Lp(V) onto the pth metabelian Lie power Mp(V). We show that the kernel of this homomorphism is a direct summand of Tp(V) and apply this result to the generic case where G is the general linear group on V and the field is infinite. In this case we find the indecomposable direct summands of Lp(V) and their multiplicities.

Item Type: | Article |
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Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 17 Nonassociative rings and algebras MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations |

Depositing User: | Ms Lucy van Russelt |

Date Deposited: | 16 Aug 2006 |

Last Modified: | 20 Oct 2017 14:12 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/512 |

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