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Nakayama automorphisms of Frobenius algebras

✍ Scribed by Will Murray

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 202 KB
Volume: 269
Category: Article
ISSN: 0021-8693
DOI: 10.1016/s0021-8693(03)00465-4

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✦ Synopsis

We show that the Nakayama automorphism of a Frobenius algebra R over a field k is independent of the field (Theorem 4). Consequently, the k-dual functor on left R-modules and the bimodule isomorphism type of the k-dual of R, and hence the question of whether R is a symmetric k-algebra, are independent of k. We give a purely ring-theoretic condition that is necessary and sufficient for a finite-dimensional algebra over an infinite field to be a symmetric algebra (Theorem 7).

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