A residue formula for the fundamental Hochschild 3-cocycle for \(SU_{q}(2)\)
type: Item
instance of: scholarly article
zbMATH Open document ID: 1247.58007
author: Ulrich Krähmer
author: A. Rennie
author: Roger Senior
publication date: 2012-06-25T00:00:00Z
full work available at URL: https://arxiv.org/abs/1105.5366
full work available at URL: jlt22024.htm
Mathematics Subject Classification ID: 58B32
Mathematics Subject Classification ID: 58B34
Mathematics Subject Classification ID: 58J42
Mathematics Subject Classification ID: 19K56
Mathematics Subject Classification ID: 46L87
Mathematics Subject Classification ID: 20G42
zbMATH DE Number: 6049467
zbMATH Keywords: spectral triples
zbMATH Keywords: Dirac operators
zbMATH Keywords: cyclic cohomology
zbMATH Keywords: quantum groups
zbMATH Keywords: quantum SU(2)
zbMATH Keywords: residue formulas
zbMATH Keywords: Calabi-Yau algebras
MaRDI profile type: Publication
arXiv ID: 1105.5366
arXiv classification: math.OA
arXiv classification: math.QA
title: A residue formula for the fundamental Hochschild 3-cocycle for \(SU_{q}(2)\)
published in: Journal of Lie Theory
review text: To describe the geometry of quantum groups and their homogeneous spaces requires that we generalise the axioms for noncommutative smooth manifolds and spectral triples. Several generalisations have been suggested in recent years. This article works out another example and constructs a variant of a spectral triple over the quantum group SU\(_q(2)\). This is not a spectral triple because the crucial axiom about bounded commutators \([D,a]\) is violated. Nevertheless, the authors manage in a somewhat ad hoc way to associate a twisted Hochschild 3-cocycle to this situation. This turns out to be the standard twisted 3-cocycle on SU\(_q(2)\). Besides the usual data used in a spectral triple, they also cut operators down with certain projections to get finite results.
reviewed by: Ralf Meyer
description: scientific article; zbMATH DE number 6049467