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 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 language | English (US) |
---|---|
Pages (from-to) | 117-154 |
Number of pages | 38 |
Journal | Algebra and Number Theory |
Volume | 10 |
Issue number | 1 |
DOIs | |
State | Published - 2016 |
Keywords
- Hopf action
- Module algebra
- Path algebra
- Schurian quiver
- Taft algebra
ASJC Scopus subject areas
- Algebra and Number Theory