The 3D Spin Geometry of the Quantum Two-Sphere
Abstract
We study a three-dimensional differential calculus on the standard Podles quantum two-sphere S2q, coming from the Woronowicz 4D+ differential calculus on the quantum group SUq(2). We use a frame bundle approach to give an explicit description of the space of forms on S2q and its associated spin geometry in terms of a natural spectral triple over S2q. 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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