Pointed Hopf Algebras with classical Weyl Groups
Shouchuan Zhang, Yao-Zhong Zhang

TL;DR
This paper classifies when Nichols algebras over classical Weyl groups are finite or infinite dimensional, providing key conditions and exceptions, which advances understanding of pointed Hopf algebras related to these groups.
Contribution
It establishes necessary and sufficient conditions for the finiteness of Nichols algebras over classical Weyl groups, identifying three specific cases of exception.
Findings
Most Nichols algebras over classical Weyl groups are infinite dimensional.
Finite dimensional Nichols algebras occur only in three specific cases.
Provides a complete characterization of finiteness conditions for these algebras.
Abstract
We prove that Nichols algebras of irreducible Yetter-Drinfeld modules over classical Weyl groups supported by are infinite dimensional, except in three cases. We give necessary and sufficient conditions for Nichols algebras of Yetter-Drinfeld modules over classical Weyl groups supported by to be finite dimensional.
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.
