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Permutability of
characters on algebras
L. Grunenfelder, R. Guralnick, T. Košir and H. Radjavi |
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Vol. 178 (1997), No. 1, 63–70
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Abstract |
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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. |
Milestones
Received: 10 June 1995
Revised: 4 January 1996
Published: 1 March 1997
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Authors |
| L. Grunenfelder | |
| Dalhousie University Halifax, Nova Scotia B3H 3J5 Canada |
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| R. Guralnick | |
| University of Southern
California Los Angeles, CA 90089-1113 |
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| T. Košir | |
| University of Ljubljana Jadranska 19 61000 Ljubljana Slovenia |
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| H. Radjavi | |
| Dalhousie University Halifax, Nova Scotia B3H 3J5 Canada |
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