Separable equivalence of rings and symmetric algebras

Abstract

We continue a study of separable equivalence from Hokkaido Mathematical Journal 24 (1995), 527-549. We prove that symmetric separable equivalent rings $A$ and $B$ are linked by a Frobenius bimodule ${}_A{P}_B$ such that $A$ is $P$-separable over $B$. Separably equivalent rings are linked by a biseparable bimodule $P$. In addition, the ring extension $A\to$ End $P_B$ is split, separable Frobenius. It is observed that left and right finite projective bimodules over symmetric algebras are Frobenius bimodules; twisted by the Nakayama automorphisms if over Frobenius algebras.

10 pages, an addendum to Hokkaido Mathematical Journal 24 (1995), 527-549, corrections and clearer arguments with thanks to the referee at Bulletin of the London Mathematics Society

References in corpus (1)

• The representation dimension of Hecke algebras and symmetric groups

Cited by in corpus (1)

• An upper bound for the representation dimension of group algebras with an elementary abelian Sylow $p$-subgroup