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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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DOI: 10.1093/qmathj/hah053

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
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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