If *A* is an Abelian group, a character is a group homomorphism into the multiplicative group of complex numbers. See also Dirichlet character.

If *f* is a representation of a group *G*, then the character of the representation is the function from *G* to the complex numbers given by the trace of *f*.

If *A* is an abelian algebra over the complex numbers, a character of *A* is an algebra homomorphism into the complex numbers. If in addition, *A* is a *-algebra, then a character is a *-homomorphism into the complex numbers.