Free Lie algebras and formal power series

Bryant, R. M. (2002) Free Lie algebras and formal power series. Journal of Algebra, 253 (1). pp. 167-188. ISSN 0021-8669

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Abstract

Let G be a group and K a field. If V is a graded KG-module of the form V=V1plus sign in circleV2plus sign in circlecdots, three dots, centered , where each Vn is finite dimensional, then the free Lie algebra L(V) acquires the structure of a graded KG-module, L(V)=L1(V)plus sign in circleL2(V)plus sign in circlecdots, three dots, centered . The isomorphism types of V and L(V) may be described by the power series ∑ngt-or-equal, slanted1[Vn]tn and ∑ngt-or-equal, slanted1[Ln(V)]tn with coefficients from the Green ring. The main object of study is the function on power series which maps ∑[Vn]tn to ∑[Ln(V)]tn for every graded KG-module V. Closed formulae are given in certain cases, and these are closely related to character formulae of Brandt and others.

Item Type: Article
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: 09 Aug 2006
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/474

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