PBW deformations of braided products
Chelsea Walton, Sarah Witherspoon
TL;DR
This paper introduces new PBW deformations of smash product algebras from Hopf algebra actions, generalizing known double constructions like Weyl and Cherednik algebras, with a focus on Koszul module algebras.
Contribution
It provides a novel framework for PBW deformations of braided products, extending existing algebraic structures and offering new examples and directions for research.
Findings
New PBW deformation examples for smash product algebras
Generalization of Weyl and Cherednik algebra constructions
Application of PBW theorem to Koszul module algebras
Abstract
We present new examples of deformations of smash product algebras that arise from Hopf algebra actions on pairs of module algebras. These examples involve module algebras that are Koszul, in which case a PBW theorem we established previously applies. Our construction generalizes several `double' constructions appearing in the literature, including Weyl algebras and some types of Cherednik algebras, and it complements the braided double construction of Bazlov and Berenstein. Many suggestions of further directions are provided at the end of the work.
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.