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The Brauer algebra has a basis of diagrams and these generate a monoid $H$consisting of scalar multiples of diagrams. Following a recent paper byKudryavtseva and Mazorchuk, we define and completely determine three types ofconjugation in $H$. We are thus able to define modular characters for Braueralgebras which share many of the properties of Brauer characters defined forfinite groups over a field of prime characteristic. Furthermore, we reformulateand extend the theory of ordinary characters for Brauer algebras as introducedby Ram to the case when the Brauer algebra is not semisimple.

Conjugation in Brauer algebras and applications to character theory