## 2006.305: Lie powers in prime degree

2006.305:
R. M. Bryant and Ralph Stöhr
(2005)
*Lie powers in prime degree.*
The Quarterly Journal of Mathematics, 56 (4).
pp. 473-489.
ISSN 0033-5606

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## 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 2000 > 17 Nonassociative rings and algebras MSC 2000 > 20 Group theory and generalizations |

MIMS number: | 2006.305 |

Deposited By: | Miss Louise Stait |

Deposited On: | 16 August 2006 |

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