The 3D Spin Geometry of the Quantum Two-Sphere

Details The 3D Spin Geometry of the Quantum Two-Sphere The 3D Spin Geometry of the Quantum Two-Sphere

2010-03-10

arxiv.org/abs/1003.2150v2

Rev. Math. Phys. 22 (2010) 963--993

Mathematics

Quantum Algebra

v2: 25 pages; minor changes

Scientific paper

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.

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