The 3D Spin Geometry of the Quantum Two-Sphere

Abstract

We study a three-dimensional differential calculus on the standard Podles quantum two-sphere S^2_q, coming from the Woronowicz 4D+ differential calculus on the quantum group SU_q(2). We use a frame bundle approach to give an explicit description of the space of forms on S^2_q and its associated spin geometry in terms of a natural spectral triple over S^2_q. We equip this spectral triple with a real structure for which the commutant property and the first order condition are satisfied up to infinitesimals of arbitrary order.

v2: 25 pages; minor changes

References in corpus (2)

• Calculi, Hodge operators and Laplacians on a quantum Hopf fibration
• The Isospectral Dirac Operator on the 4-dimensional Orthogonal Quantum Sphere

Cited by in corpus (5)

• Quantum Bundle Description of the Quantum Projective Spaces
• Calculi, Hodge operators and Laplacians on a quantum Hopf fibration
• (A class of) Hodge duality operators over the quantum SU(2)
• Differential and Twistor Geometry of the Quantum Hopf Fibration
• A Note on Gluing Dirac Type Operators on a Mirror Quantum Two-Sphere