Character ring

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Template:Functor from groups

Definition

Definition with symbols

Given a group G, a field k, and a subring R of k, the character ring of G with respect to k and R, is the ring of R-linear combinations of characters of representations of G over k.

If R is not specified, we assume it to be the smallest subring (viz the subring generated by 1, which is either \Z or a prime field of the same characteristic as the whole field).