Character (group theory)

In group theory, a character may refer one of two related concepts: a group homomorphism from a group to the unit circle, or the trace of a group representation.

Group homomorphism
A character of a group G is a group homomorphism from G to the unit circle, the multiplicative group of complex numbers of modulus one.

Group representation
A character of a group representation of G, which may be regarded as a homomorphism from the group G to a matrix group, is the trace of the corresponding matrix.