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.

arXiv comment14 pages

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Cited by in corpus (17)

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• The Podles spheres converge to the sphere
• Asymptotic and exact expansions of heat traces
• Heat trace and spectral action on the standard Podles sphere
• Spectral Action in Noncommutative Geometry
• On the Chern-Gauss-Bonnet Theorem and Conformally Twisted Spectral Triples for $C^{\ast }$-Dynamical Systems
• Noncommutative Geometry and Conformal Geometry. III. Vafa-Witten Inequality and Poincaré Duality
• On modular semifinite index theory
• Quantum Dimension and Quantum Projective Spaces
• On the spectral and homological dimension of k-Minkowski space
• 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
• Zeta-regularization and the heat-trace on some compact quantum semigroups