Actions of some pointed Hopf algebras on path algebras of quivers

Abstract

We classify Hopf actions of Taft algebras T(n) on path algebras of quivers, in the setting where the quiver is loopless, finite, and Schurian. As a corollary, we see that every quiver admitting a faithful Z_n-action (by directed graph automorphisms) also admits inner faithful actions of a Taft algebra. Several examples for actions of the Sweedler algebra T(2) and for actions of T(3) are presented in detail. We then extend the results on Taft algebra actions on path algebras to actions of the Frobenius-Lusztig kernel u_q(sl_2), and to actions of the Drinfeld double of T(n).

29 pages. v3: Title changed, and Section 8 is new

References in corpus (1)

• Algebras simple with respect to a Taft algebra action

Cited by in corpus (14)

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• Actions of Ore extensions and growth of polynomial $H$-identities
• Pointed Hopf actions on quantum generalized Weyl algebras
• Isomorphisms of graded path algebras
• Several locality semigroups, path semigroups and partial semigroups
• Classifying partial (co)actions of Taft and Nichols Hopf algebras on their base fields
• Prime and semiprime quantum linear space smash products
• Braided commutative algebras over quantized enveloping algebras
• Auslander's Theorem for dihedral actions on preprojective algebras of type A
• (Co)module algebras and their generalizations