
Journal of Lie Theory 22 (2012), No. 2, 557585 Copyright Heldermann Verlag 2012 A Residue Formula for the Fundamental Hochschild 3Cocycle for SU_{q}(2) Ulrich Krähmer School of Mathematics & Statistics, University of Glasgow, 15 University Gardens, Glasgow G12 8QW, Scotland ulrich.kraehmer@glasgow.ac.uk Adam Rennie Mathematical Sciences Institute, Australian National University, Acton, ACT 0200, Australia adam.rennie@anu.edu.au Roger Senior Mathematical Sciences Institute, Australian National University, Acton, ACT 0200, Australia roger.senior@anu.edu.au An analogue of a spectral triple over SU_{q}(2) is constructed for which the usual assumption of bounded commutators with the Dirac operator fails. An analytic expression analogous to that for the Hochschild class of the Chern character for spectral triples yields a nontrivial twisted Hochschild 3cocycle. The problems arising from the unbounded commutators are overcome by defining a residue functional using projections to cut down the Hilbert space. Keywords: Spectral triples, Dirac operators, cyclic cohomology, quantum groups, quantum SU(2), residue formulas, CalabiYau algebras. MSC: 19K33, 19K56, 20G42, 46L80, 46L87,; 58B32, 58B34, 58J42, 58J20, 81R50 [ Fulltextpdf (399 KB)] for subscribers only. 