Nakayama automorphisms of Frobenius algebras

[摘要] 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). (C) 2003 Elsevier Inc. All rights reserved.

[发布日期] 2003-11-15

[关键词] Nakayama automorphism;Frobenjus algebra;Frobenius ring;symmetric algebra;dual module;dual functor;bimodule;Brauer equivalence