Pointed Hopf algebras with classical Weyl groups.
type: Item
instance of: scholarly article
zbMATH Open document ID: 1255.16038
DOI: 10.1142/S0129167X12500668
author: Shouchuan Zhang
author: Yao-Zhong Zhang
published in: International Journal of Mathematics
publication date: 2012-06-04T00:00:00Z
full work available at URL: https://arxiv.org/abs/0910.1280
Mathematics Subject Classification ID: 16T05
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 6042652
zbMATH Keywords: pointed Hopf algebras
zbMATH Keywords: Nichols algebras
zbMATH Keywords: Yetter-Drinfeld modules
zbMATH Keywords: Weyl groups
zbMATH Keywords: symmetric groups
MaRDI profile type: Publication
arXiv ID: 0910.1280
cites work: On pointed Hopf algebras associated with the symmetric groups.
cites work: Q3153375
cites work: On pointed Hopf algebras associated to some conjugacy classes in 𝕊_{𝕟}
cites work: Q5580319
cites work: The Weyl groupoid of a Nichols algebra of diagonal type
cites work: Root systems and Weyl groupoids for Nichols algebras
OpenAlex ID: W3099085916
title: Pointed Hopf algebras with classical Weyl groups.
review text: Let \(\mathbb S_n\) denote the symmetric group of degree \(n>2\) and let \(G=A\rtimes\mathbb S_n\) be a classical Weyl group, where \(A\subseteq\mathbb Z_2^n\). In the paper under review the authors give a necessary and sufficient condition for a Nichols algebra of an irreducible Yetter-Drinfeld module \(V\) over \(G\) supported by \(A\) to be finite dimensional. It is shown that Nichols algebras of irreducible Yetter-Drinfeld modules over \(G\) supported by \(\mathbb S_n\) are infinite dimensional, except in three cases. Related results on Nichols algebras over symmetric groups appeared in the paper [Ann. Mat. Pura Appl. (4) 190, No. 2, 225-245 (2011; Zbl 1234.16019)], by \textit{N. Andruskiewitsch, F. Fantino, M. Graña} and \textit{L. Vendramin}.
reviewed by: Sonia Natale
description: scientific article; zbMATH DE number 6042652