PERMUTABILITY OF CHARACTERS ON ALGEBRAS

An algebra of matrices A with Jacobson radical R is said to have permu table trace if Tr(abc) = Tr(bac) for all a,b,c in A. We show in this p aper that in characteristic zero A has permutable trace if and only if A/R is commutative. Generalizing to arbitrary characteristic we find that the result still holds when the trace form of A is nora-degenerat e. Finally, in positive characteristic, slightly stronger condition of permutability of the Brauer character is shown to be equivalent to th e commutativity of A/R.