On the Koszul formula in noncommutative geometry

Article Type

Research Article

Publication Title

Reviews in Mathematical Physics

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.

DOI

10.1142/S0129055X20500324

Publication Date

11-1-2020

Comments

Open Access, Green

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