Permutability of characters on algebras

L. Grünenfelder, Robert M. Guralnick, Tomaž Košir, Heydar Radjavi

Type: Article

Publication Date: 1997-03-01

Citations: 7

DOI: https://doi.org/10.2140/pjm.1997.178.63

Abstract

An algebra of matrices A with Jacobson radical R is said to have permutable trace if Tr(abc) = Tr(bac) for all a, b, c in A. We show in this paper 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 non-degenerate.Finally, in positive characteristic, slightly stronger condition of permutability of the Brauer character is shown to be equivalent to the commutativity of A/R.

Locations

Pacific Journal of Mathematics - View - PDF

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