Character of a linear representation

From Groupprops
(Redirected from Character)
Jump to: navigation, search

This term makes sense in the context of a linear representation of a group, viz an action of the group as linear automorphisms of a vector space


This article gives a basic definition in the following area: linear representation theory
View other basic definitions in linear representation theory |View terms related to linear representation theory |View facts related to linear representation theory

Definition

Definition in terms of linear representation as a homomorphism

Let G be a group and \rho: G \to GL(V) be a finite-dimensional linear representation over a field k. Then, the character of \rho is the composite Tr \circ \rho where Tr is the trace map from GL(V) to k.

Definition in terms of linear representation as an algebra map