Dirac operator and a twisted cyclic cocycle on the standard Podles quantum sphere

Abstract

A Dirac operator D on the standard Podles sphere is defined and investigated. It yields a spectral triple such that |D|^{-z} is of trace class for Re z>0. Commutators with the Dirac operator give the distinguished 2-dimensional covariant differential calculus on the standard Podles sphere. The twisted cyclic cocycle associated with the volume form of the differential calculus is expressed by means of the Dirac operator.

21 pages

References in corpus (1)

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

Cited by in corpus (15)

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• The Podles sphere as a spectral metric space
• The 3D Spin Geometry of the Quantum Two-Sphere
• The Hochschild cohomology ring of the standard Podles quantum sphere
• Equivariant Fredholm modules for the full quantum flag manifold of $S{U}_q(3)$
• On the noncommutative spin geometry of the standard Podles sphere and index computations
• Twisted Homology of Quantum SL(2) - Part II
• The resolvent cocycle in twisted cyclic cohomology and a local index formula for the Podles sphere
• Noncommutative Geometry and Quantum Group Symmetries
• Twisted sigma-model solitons on the quantum projective line