Spectral triples and associated Connes-de Rham complex for the quantum SU(2) and the quantum sphere

Abstract

We construct spectral triples for the C^*-algebra of continuous functions on the quantum SU(2) group and the quantum sphere. There has been various approaches towards building a calculus on quantum spaces, but there seems to be very few instances of computations outlined in chapter~6 of Connes' book. We give detailed computations of the associated Connes-de Rham complex and the space of L_2-forms.

LaTeX2e, 11 pages

References in corpus (1)

• Cyclic Cohomology, Quantum group Symmetries and the Local Index Formula for SUq(2)

Cited by in corpus (12)

• Symmetries of Lévy processes on compact quantum groups, their Markov semigroups and potential theory
• Twisted cyclic homology of all Podles quantum spheres
• Local Index Formula on the Equatorial Podles Sphere
• Geometry of Quantum Spheres
• Quantum Group of Orientation preserving Riemannian Isometries
• Spectral action on SU_q(2)
• Lectures on Differential Geometry of Modules and Rings
• Some counterexamples in the theory of quantum isometry groups
• Characterization of spectral triples: A combinatorial approach
• On some algebraic and geometric aspects of the quantum unitary group
• Characterization of $S{U}_q(\ell +1)$-equivariant spectral triples for the odd dimensional quantum spheres
• Torus equivariant spectral triples for odd dimensional quantum spheres coming from $C^{\ast }$-extensions