Brauer character

Summary

A Brauer character is the analogue of the character of a representation for representations of a finite group over a field of prime characteristic $p$. It is a complex-valued function on the elements of order prime to $p$. Its values come from lifting the eigenvalues of each matrix to complex roots of unity. Brauer characters determine the composition factors of a modular representation, which ordinary traces in characteristic $p$ cannot do. They are the basic tool of modular representation theory.