Nakayama automorphisms of Frobenius algebras

JOURNAL OF ALGEBRA

卷:269

Article

Murray, W

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

DOI  :  10.1016/S0021-8693(03)00465-4

来源: Elsevier

【 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.

【 授权许可】

Free