We prove a Koszul formula for the Levi-Civita connection for any pseudo-Riemannian bilinear metric on a class of centered bimodule of noncommutative one-forms. As an application to the Koszul formula, we show that our Levi-Civita connection is a bimodule connection. We construct a spectral triple on a fuzzy sphere and compute the scalar curvature for the Levi-Civita connection associated to a canonical metric.
On the Koszul formula in noncommutative geometry / Bhowmick, Jyotishman; Goswami, Debashish; Landi, Giovanni. - In: REVIEWS IN MATHEMATICAL PHYSICS. - ISSN 0129-055X. - 32:(2020), pp. 2050032-2050064. [10.1142/S0129055X20500324]
On the Koszul formula in noncommutative geometry
Landi, Giovanni
2020-01-01
Abstract
We prove a Koszul formula for the Levi-Civita connection for any pseudo-Riemannian bilinear metric on a class of centered bimodule of noncommutative one-forms. As an application to the Koszul formula, we show that our Levi-Civita connection is a bimodule connection. We construct a spectral triple on a fuzzy sphere and compute the scalar curvature for the Levi-Civita connection associated to a canonical metric.| File | Dimensione | Formato | |
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