Let G be a group and K a field. If V is a graded KG-module of the form V = V-1 circle plus V2 circle plus ..., where each V-n is finite dimensional, then the free Lie algebra L(V) acquires the structure of a graded KG-module, L(V) = L-1 (V) circle plus L-2(V) circle plus .... The isomorphism types of V and L(V) may be described by the power series Sigma(ngreater than or equal to1) [V-n]t(n) and Sigma(ngreater than or equal to1) [L-n(V)]t(n) with coefficients from the Green ring. The main object of study is the function on power series which maps Sigma[V-n]t(n) to Sigma[L-n(V)]t(n) 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. (C) 2002 Elsevier Science (USA). All rights reserved. [References: 18]
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