Actions of Taft's algebras on finite dimensional algebras

Abstract

Let F be a field containing a primitive m-th root of the unit. We characterize the actions of a Taft's algebra Hm of a certain order m on finite dimensional arbitrary algebras. We describe the action in terms of gradings and actions by skew-derivations. Moreover we prove the associative algebra UT2 of 2×2 upper triangular matrices with entries from F does not generate a variety of Hm-module algebras of almost polynomial growth.