We study a three-dimensional differential calculus on the standard quantum two-sphere Sq2, coming from the 4D+ differential calculus on the quantum group SUq(2). We use a frame bundle approach to give an explicit description of Ω1Sq2 and its associated spin geometry in terms of a natural spectral triple over the sphere. 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.
The 3D Spin Geometry of the Quantum Two-Sphere / Brain, S., Landi, G.. - In: REVIEWS IN MATHEMATICAL PHYSICS. - ISSN 0129-055X. - STAMPA. - 22:(2010), pp. 963-993. [10.1142/S0129055X10004119]
The 3D Spin Geometry of the Quantum Two-Sphere
LANDI, GIOVANNI
2010-01-01
Abstract
We study a three-dimensional differential calculus on the standard quantum two-sphere Sq2, coming from the 4D+ differential calculus on the quantum group SUq(2). We use a frame bundle approach to give an explicit description of Ω1Sq2 and its associated spin geometry in terms of a natural spectral triple over the sphere. 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.Pubblicazioni consigliate
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