A twisted spectral triple for quantum SU(2)

Details A twisted spectral triple for quantum SU(2) A twisted spectral triple for quantum SU(2)

2011-09-11

arxiv.org/abs/1109.2326v1

Mathematics

Quantum Algebra

14 pages

Scientific paper

We initiate the study of a q-deformed geometry for quantum SU(2). In contrast with the usual properties of a spectral triple, we get that only twisted commutators between algebra elements and our Dirac operator are bounded. Furthermore, the resolvent only becomes compact when measured with respect to a trace on a semifinite von Neumann algebra which does not contain the quantum group. We show that the zeta function at the identity has a meromorphic continuation to the whole complex plane and that a large family of local Hochschild cocycles associated with our twisted spectral triple are twisted coboundaries.

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