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arXiv · 1003.2150

The 3D Spin Geometry of the Quantum Two-Sphere

Simon Brain·Giovanni Landi
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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.

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Simon Brain, Giovanni Landi. 2010-09-30. The 3D Spin Geometry of the Quantum Two-Sphere. https://doi.org/10.1142/s0129055x10004119

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