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2006.268: Free Lie algebras and formal power series

2006.268: R. M. Bryant (2002) Free Lie algebras and formal power series. Journal of Algebra, 253 (1). pp. 167-188. ISSN 0021-8669

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DOI: 10.1016/S0021-8693(02)00068-6

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 2000 > 17 Nonassociative rings and algebras
MSC 2000 > 20 Group theory and generalizations
MIMS number:2006.268
Deposited By:Miss Louise Stait
Deposited On:09 August 2006

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