Lie algebras simple with respect to a Taft algebra action

We classify finite dimensional Hm2(ζ)-simple Hm2(ζ)-module Lie algebras L over an algebraically closed field of characteristic 0 where Hm2(ζ) is the mth Taft algebra. As an application, we show that despite the fact that L can be non-semisimple in ordinary sense, limn→∞⁡cnHm2(ζ)(L)n=dim⁡L where cnHm2(ζ)(L) is the codimension sequence of polynomial Hm2(ζ)-identities of L. In particular, the analog of Amitsur's conjecture holds for cnHm2(ζ)(L).