On the Koszul formula in noncommutative geometry-Reference-Cited by-同舟云学术

On the Koszul formula in noncommutative geometry

Published:2020-05-12 Issue:10 Volume:32 Page:2050032
ISSN:0129-055X
Container-title:Reviews in Mathematical Physics
language:en
Short-container-title:Rev. Math. Phys.

Author:

Bhowmick Jyotishman¹²,Goswami Debashish¹²,Landi Giovanni³²^ORCID

Affiliation:

1. Indian Statistical Institute, 203, B. T. Road, Kolkata 700108, India

2. Institute for Geometry and Physics (IGAP) Trieste, Italy and INFN, Trieste, Italy

3. Matematica, Università di Trieste, Via A. Valerio, 12/1, 34127 Trieste, Italy

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129055X20500324

Reference21 articles.

1. Riemannian curvature of the noncommutative 3-sphere

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3. ∗-compatible connections in noncommutative Riemannian geometry

4. Levi-Civita connections for a class of spectral triples

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