Let G be a group, K a field and V a finite-dimensional KG- module. Let L(V) denote the free Lie algebra on the K-space V and, for each positive integer N, let L~n(V) be the homogeneous component of degree n in L(V). The action of G on V extends naturally to L(V), so that G acts on L(V) by Lie algebra automorphisms. In this way L (V) becomes a KG- module with each L~n(V) as a submodule, called the n th Lie power of V.
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