Algebras simple with respect to a Taft algebra action. (Q2341536)

Let \(F\) be a field and let \(H\) be a Taft Hopf algebra over \(F\). A left \(H\)-module algebra \(A\) is called \(H\)-simple if \(A^2\neq 0\) and \(A\) has no non-trivial two-sided \(H\)-invariant ideals. For algebraically closed \(F\), the author classifies all semisimple \(H\)-simple module algebras, and for a perfect field \(F\), he classifies the finite dimensional non-semisimple \(H\)-simple module algebras. If \(F\) is an algebraically closed field of characteristic zero, an analog of Amitsur's conjecture for codimensions of polynomial \(H\)-identities of finite dimensional \(H\)-simple module algebras is proved.