Lie algebras simple with respect to a Taft algebra action

Abstract

We classify finite dimensional H m 2 (ζ)-simple H m 2 (ζ)-module Lie algebras L over an algebraically closed field of characteristic 0 where H m 2 (ζ) is the mth Taft algebra. As an application, we show that despite the fact that L can be non-semisimple in ordinary sense, lim n→∞ n cis the codimension sequence of polynomial H m 2 (ζ)-identities of L. In particular, the analog of Amitsur's conjecture holds for cas H m 2 (ζ)-module Lie algebras for α = 0. In Theorem 5.1 we prove that every non-semisimple H m 2 (ζ)-simple Lie algebra is

Varieties of Null-Filiform Leibniz Algebras Under the Action of Hopf Algebras

“…It is easy to see Taft's algebras are not semisimple algebras. Also the result by Gordienko [30] is another good step in this direction. In fact, he proved the existence of the exponent for finite dimensional algebras over an algebraically closed field of characteristic 0 that are simple under the action of a Taft algebra.…”

Specht property for the algebra of upper triangular matrices of size two with a Taft’s algebra action

“…It is easy to see that Taft’s algebras are not semisimple algebras. In [24], the author proved the existence of the exponent for finite dimensional algebras over an algebraically closed field of characteristic 0 that are simple under the action of a Taft’s algebra. We recall Taft’s algebras are noncommutative, noncocommutative, and not semisimple Hopf algebras.…”