Algebras simple with respect to a Taft algebra action

Abstract

Algebras simple with respect to an action of a Taft algebra $H_{m^2}(\zeta )$ deliver an interesting example of $H$-module algebras that are $H$-simple but not necessarily semisimple. We describe finite dimensional $H_{m^2}(\zeta )$-simple algebras and prove the analog of Amitsur's conjecture for codimensions of their polynomial $H_{m^2}(\zeta )$-identities. In particular, we show that the Hopf PI-exponent of an $H_{m^2}(\zeta )$-simple algebra $A$ over an algebraically closed field of characteristic $0$ equals $\dim A$. The groups of automorphisms preserving the structure of an $H_{m^2}(\zeta )$-module algebra are studied as well.

13 pages. This article is a generalization of arXiv:1309.3664

References in corpus (1)

• Actions of some pointed Hopf algebras on path algebras of quivers

Cited by in corpus (7)

• Actions of some pointed Hopf algebras on path algebras of quivers
• Lie algebras simple with respect to a Taft algebra action
• Equivalences of (co)module algebra structures over Hopf algebras
• On $H$-simple not necessarily associative algebras
• Actions of Ore extensions and growth of polynomial $H$-identities
• Group Gradings and Actions of Pointed Hopf Algebras
• (Co)module algebras and their generalizations