Journal article
Actions of some pointed Hopf algebras on path algebras of quivers
Algebra & Number Theory, Vol.10(1), pp.117-154
01/01/2016
DOI: 10.2140/ant.2016.10.117
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).
Details
- Title: Subtitle
- Actions of some pointed Hopf algebras on path algebras of quivers
- Creators
- Ryan Kinser - University of IowaChelsea Walton - Temple University
- Resource Type
- Journal article
- Publication Details
- Algebra & Number Theory, Vol.10(1), pp.117-154
- Publisher
- MATHEMATICAL SCIENCE PUBL
- DOI
- 10.2140/ant.2016.10.117
- ISSN
- 1937-0652
- eISSN
- 1944-7833
- Number of pages
- 38
- Grant note
- DMS-1550306 / National Science Foundation: NSF-grant
- Language
- English
- Date published
- 01/01/2016
- Academic Unit
- Mathematics
- Record Identifier
- 9984241052402771
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