Definition. character [2601]

A character $\chi$ of a group $G$ with values in a field $L$ is a homomorphism from $G$ to the multiplicative group $L^{\times}$, i.e. a function $\chi : G \to L^{\times}$ such that $\chi(g_{1})\chi(g_{2}) = \chi(g_{1}g_{2})$ for all $g_{1}, g_{2} \in G$.