Actions of some pointed Hopf algebras on path algebras of quivers

Ryan Kinser, Chelsea Walton

Research output: Contribution to journalArticlepeer-review


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 Zn -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 uq (sl2), and to actions of the Drinfeld double of T(n).

Original languageEnglish (US)
Pages (from-to)117-154
Number of pages38
JournalAlgebra and Number Theory
Issue number1
StatePublished - 2016


  • Hopf action
  • Module algebra
  • Path algebra
  • Schurian quiver
  • Taft algebra

ASJC Scopus subject areas

  • Algebra and Number Theory


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