Journal of Lie Theory

no. 2
A Residue Formula for the Fundamental Hochschild 3-Cocycle for SUq(2)
Ulrich Krähmer1; Adam Rennie2; Roger Senior2
1School of Mathematics & Statistics, University of Glasgow, 15 University Gardens, Glasgow G12 8QW, Scotland
2Mathematical Sciences Institute, Australian National University, Acton, ACT 0200, Australia
Journal of Lie Theory, Volume 22 (2012) no. 2, pp. 557-585
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.
DOI: 10.5802/jolt.682
Classification: 19K33, 19K56, 20G42, 46L80, 46L87,, 58B32, 58B34, 58J42, 58J20, 81R50
Keywords: Spectral triples, Dirac operators, cyclic cohomology, quantum groups, quantum SU(2), residue formulas, Calabi-Yau algebras

Ulrich Krähmer  1 ; Adam Rennie  2 ; Roger Senior  2

1 School of Mathematics & Statistics, University of Glasgow, 15 University Gardens, Glasgow G12 8QW, Scotland
2 Mathematical Sciences Institute, Australian National University, Acton, ACT 0200, Australia 
Ulrich Krähmer; Adam Rennie; Roger Senior. A Residue Formula for the Fundamental Hochschild 3-Cocycle for SUq(2). Journal of Lie Theory, Volume 22 (2012) no. 2, pp. 557-585. doi: 10.5802/jolt.682
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     journal = {Journal of Lie Theory},
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