Classifying Nichols algebras over classical Weyl groups

TL;DR

This paper proves that conjugacy classes of classical Weyl groups are of type D, leading to the conclusion that Nichols algebras over these groups are infinite dimensional for certain cases, advancing understanding in algebraic structures.

Contribution

It establishes the type D classification of conjugacy classes in classical Weyl groups and shows the resulting infinite dimensionality of Nichols algebras over these groups.

Findings

Conjugacy classes of $W(B_{n})$ and $W(D_{n})$ are of type D.

Nichols algebras over classical Weyl groups $ ext{for } n ext{≥} 5$ are infinite dimensional.

Provides new insights into the structure of Nichols algebras over Weyl groups.

Abstract

In this article, we show that conjugacy classes of classical Weyl groups $W(B_{n})$ and $W(D_{n})$ are of $\textit{type D}$. Consequently, we obtain that Nichols algebras of irreducible Yetter-Drinfeld modules over the classical Weyl groups $\mathbb W_{n}$ ($n\geq5$) are infinite dimensional.