Frobenius Modules Associated to Algebra Automorphisms

Abstract

Here, we study Frobenius bimodules associated with a pair of automorphisms of an algebra and discuss their basic properties. In particular, some equivalent conditions for a finite-dimensional bimodule are proved to be Frobenius and some isomorphisms between Ext-groups and Tor-groups of Frobenius modules over finite dimensional algebras are established.

Keywords

• Frobenius module
• ext-group
• tor-group