Nichols algebras over classical Weyl groups

TL;DR

This paper investigates Nichols algebras over classical Weyl groups, showing most conjugacy classes are of type D and most Nichols algebras are infinite dimensional, with a few exceptions.

Contribution

It identifies specific cases where Nichols algebras over classical Weyl groups are finite dimensional, advancing understanding of their structure.

Findings

Most conjugacy classes in classical Weyl groups are of type D.

Most Nichols algebras over these groups are infinite dimensional.

Finite dimensional Nichols algebras occur only in specific cases.

Abstract

We show that except in several cases conjugacy classes of classical Weyl groups $W(B_n)$ and $W(D_n)$ are of type {\rm D}. We prove that except in three cases Nichols algebras of irreducible Yetter-Drinfeld ({\rm YD} in short )modules over the classical Weyl groups are infinite dimensional.