Actions of Hopf-Ore Extensions of Group Algebras on Path Algebras of Quivers
Elise Askelsen, Ryan Kinser
TL;DR
This paper classifies how Hopf-Ore extensions of group algebras act on path algebras of quivers, extending previous results to a more general setting and demonstrating applications to specific Hopf algebras.
Contribution
It provides a comprehensive classification of Hopf actions on path algebras for a broad class of Hopf-Ore extensions, generalizing earlier special case results.
Findings
Classification of filtered Hopf actions on path algebras
Extension of results to general Hopf-Ore extensions
Applications to Noetherian prime Hopf algebras of low GK-dimension
Abstract
We classify the (filtered) Hopf actions of Hopf-Ore extensions of group algebras on path algebras of quivers, extending results in several other works from special cases to this general setting. Having done this for general Hopf-Ore extensions of group algebras, we demonstrate application by specializing our main result to certain Hopf-Ore extensions including some Noetherian prime Hopf algebras of GK-dimension one and two.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Logic · Topological and Geometric Data Analysis