Journal of Lie Theory 22 (2012), No. 2, 557--585
Copyright Heldermann Verlag 2012
A Residue Formula for the Fundamental Hochschild 3-Cocycle for SUq(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 SUq(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 non-trivial twisted Hochschild 3-cocycle. 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, Calabi-Yau algebras.
MSC: 19K33, 19K56, 20G42, 46L80, 46L87,; 58B32, 58B34, 58J42, 58J20, 81R50
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