Twisted cyclic homology of all Podles quantum spheres

Abstract

We calculate the twisted Hochschild and cyclic homology (in the sense of Kustermans, Murphy and Tuset) of all Podles quantum spheres relative to arbitary automorphisms. Our calculations are based on a free resolution due to Masuda, Nakagami and Watanabe. The dimension drop in Hochschild homology can be overcome by twisting by automorphisms induced from the canonical modular automorphism associated to the Haar state on quantum SU(2). We specialize our results to the standard quantum sphere, and identify the class in twisted cyclic cohomology of the 2-cocycle discovered by Schmuedgen and Wagner corresponding to the distinguished covariant differential calculus found by Podles.

17 pages, no figures, uses the amscd package. v6: final version accepted for publication

References in corpus (4)

• A Local Index Formula for the Quantum Sphere
• Spectral triples and associated Connes-de Rham complex for the quantum SU(2) and the quantum sphere
• Commutator Representations of Differential Calculi on the Quantum Group SU_q(2)
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Cited by in corpus (18)

• Holomorphic structures on the quantum projective line
• The Hochschild cohomology ring of the standard Podles quantum sphere
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• On the Hochschild (co)homology of Quantum Homogeneous Spaces
• The resolvent cocycle in twisted cyclic cohomology and a local index formula for the Podles sphere
• A residue formula for the fundamental Hochschild class of the Podles sphere
• Quantum Dimension and Quantum Projective Spaces
• On the spectral and homological dimension of k-Minkowski space
• Braided homology of quantum groups
• Twisted Cyclic Cohomology and Modular Fredholm Modules
• Noncommutative Geometry and Quantum Group Symmetries
• Homological smoothness and deformations of generalized Weyl algebras
• Twisted homology of quantum SL(2)
• Twisted Hochschild Homology of Quantum Flag Manifolds and Kähler Forms
• A characteristic map for compact quantum groups
• Noncommutative Kahler Geometry of the Standard Podles Sphere
• Twisted Hochschild homology of quantum flag manifolds: 2-cycles from invariant projections
• Twisted sigma-model solitons on the quantum projective line