2-cocycles and twisting of Kac algebras
type: Item
instance of: scholarly article
title: 2-cocycles and twisting of Kac algebras
zbMATH Open document ID: 0946.46058
author: Leonid Vainerman
published in: Communications in Mathematical Physics
publication date: 2000-02-06T00:00:00Z
review text: The paper describes twisting of Hopf-von Neumann and Kac algebras by 2-cocycles, and can be viewed as a generalisation of [\textit{M. Enock} and \textit{L. Vainerman}, Commun. Math. Phys. 178, No. 3, 571-596 (1996; Zbl 0876.46042)]. It is shown that in the case of a Kac algebra, if the twisting 2-cocycle is lifted from a 2-cocycle on a locally compact subgroup whose image belongs to the centralizer of the Haar weight, then the coinvolutive Hopf-von Neumann algebra with undeformed Haar weight obtained by twisting is a Kac algebra. Quantisations of the Heisenberg group and several series of \(C^*\)-Hopf algebras of finite dimensions \(4n\) and \(2n^2\) obtained by twisting of finite groups are given as examples.
Mathematics Subject Classification ID: 46L89
Mathematics Subject Classification ID: 16W30
zbMATH DE Number: 1213872
zbMATH Keywords: Kac algebras
zbMATH Keywords: Hopf algebras
zbMATH Keywords: von Neumann algebras
zbMATH Keywords: twisting
zbMATH Keywords: coinvolutive Hopf-von Neumann algebra with undeformed Haar weight
reviewed by: Tomasz Brzeziński
MaRDI profile type: Publication
full work available at URL: s002200050284
OpenAlex ID: W2007150554
DOI: 10.1007/S002200050284
description: scientific article; zbMATH DE number 1213872