On the Koszul formula in noncommutative geometry
arXiv:1910.09306 · doi:10.1142/S0129055X20500324
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.
arXiv commentTo appear in Reviews in Mathematical Physics
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Cited by in corpus (6)
- Gauge theories on quantum spaces
- Levi-Civita connections and vector fields for noncommutative differential calculi
- Cartan structure equations and Levi-Civita connection in noncommutative geometry
- Levi-Civita connections on quantum spheres
- Quantum Riemannian geometry of quantum projective spaces
- Levi-Civita connections from toral actions