A twisted spectral triple for quantum SU(2)

Abstract

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.

14 pages

References in corpus (3)

• Type III and spectral triples
• KK-theory and Spectral Flow in von Neumann Algebras
• A residue formula for the fundamental Hochschild class of the Podles sphere

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• Spectral Action in Noncommutative Geometry
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• Noncommutative Geometry and Conformal Geometry. III. Vafa-Witten Inequality and Poincaré Duality
• On modular semifinite index theory
• Quantum Dimension and Quantum Projective Spaces
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• Twisted Cyclic Cohomology and Modular Fredholm Modules
• Non-commutative integration, zeta functions and the Haar state for $S{U}_q(2)$
• Index map, $\sigma$-connections, and Connes-Chern character in the setting of twisted spectral triples
• A twisted local index formula for curved noncommutative two tori
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