Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Classifying Nichols algebras over classical Weyl groups

Weicai Wu, Panyue Zhou

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.

Classifying Nichols algebras over classical Weyl groups

Abstract

In this article, we show that conjugacy classes of classical Weyl groups and are of . Consequently, we obtain that Nichols algebras of irreducible Yetter-Drinfeld modules over the classical Weyl groups () are infinite dimensional.

Paper Structure

This paper contains 3 sections, 11 theorems, 6 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Main results

Key Result

Theorem 3.1

11 Assume $n\ge 5$. Let $\sigma\in\mathbb S_{n}$ be of type $(1^{m_{1}},2^{m_{2}},\dots,n^{m_{n}})$ and $a\in H_{n}$ with $a\sigma\in \mathbb W_{n}$ and $\sigma\not=1$. If dim $\mathfrak B(\mathcal{O}_{a\sigma}^{\mathbb W_{n}}, \rho)<\infty$, then the type of $\sigma$ belongs to one in the following

Theorems & Definitions (12)

  • Theorem 3.1
  • Theorem 3.2
  • Lemma 3.3
  • Proposition 3.4
  • Lemma 3.5
  • Proposition 3.6
  • Proposition 3.7
  • Proposition 3.8
  • Proposition 3.9
  • Theorem 3.10
  • ...and 2 more