Character (group theory)

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This editable Main Article is under development and subject to a disclaimer.

[edit intro]

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[edit]

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[edit]

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.

## See also[edit]

* Dirichlet character