Abstract
In 1942 Thrall (3) introduced what he called the Lie character to study the structure of the free Lie ring. These characters are defined by associative representations of the full linear group GL q(C). Their importance is seen in the fact that, for each n, the splitting of the submodule of Lie forms of degree n into irreducible invariant subspaces is completely specified by the Lie character ζn.

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