Constructing quantum groups and Hopf algebras from coverings
type: Item
instance of: scholarly article
title: Constructing quantum groups and Hopf algebras from coverings
zbMATH Open document ID: 0837.16036
published in: Journal of Algebra
publication date: 1996-03-04T00:00:00Z
review text: Let \(G\) be a finite group, \(W:\{1,\dots, n\} \to G\) a weight function, \(\Gamma\) the directed graph associated to \(W\) and \(K\Gamma\) the corresponding path algebra over a field \(K\). If the image of \(W\) is contained in the center of \(G\), then any choice of multiplicative characters \(f_i:G \to K^\times\), \(1 \leq i \leq n\), determines a Hopf algebra structure on the path algebra \(K \Gamma\). If \(f_i(W_j)=f_j(W_i)^{-1}\) for \(i \neq j\) then \(K \Gamma\) has a finite dimensional Hopf algebra quotient. This construction generalizes that given by \textit{C. Cibils} [Commun. Math. Phys. 157, No. 3, 459-477 (1993; Zbl 0806.16039)].
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 16G20
zbMATH DE Number: 802367
zbMATH Keywords: finite groups
zbMATH Keywords: weight functions
zbMATH Keywords: directed graphs
zbMATH Keywords: path algebras
zbMATH Keywords: multiplicative characters
zbMATH Keywords: Hopf algebras
zbMATH Keywords: finite dimensional Hopf algebra quotients
author: E. L. Green
reviewed by: Nicolás Andruskiewitsch
MaRDI profile type: Publication
full work available at URL: jabr.1995.1231
OpenAlex ID: W2011587966
DOI: 10.1006/JABR.1995.1231
description: scientific article; zbMATH DE number 802367