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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Invariant traces on algebras

Author: Guido Karrer
Journal: Proc. Amer. Math. Soc. 42 (1974), 369-372
MSC: Primary 16A64
MathSciNet review: 0327838
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Abstract: Certain properties of traces on a finite-dimensional associative algebra A lead to the definition of an element $ t(A) \in {H^1}({\text{Out}}\;A,{C^\ast}),{C^\ast}$ being the multiplicative group of the center of A as Out A-module. It is shown that $ t(A) = 0$ is equivalent to the existence of nondegenerate traces on A which are invariant under composition with all automorphisms of A. In particular, by means of Galois theory, $ t(A) = 0$ is shown for a semisimple algebra A, whereas $ t(A) \ne 0$ for certain group algebras.

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Keywords: Trace on algebras, semisimple algebra, group algebra, cohomology of groups, automorphism of a group algebra
Article copyright: © Copyright 1974 American Mathematical Society