On the Koszul formula in noncommutative geometry
Quantum Algebra
2020-05-07 v2 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.1910.09306,
title = {On the Koszul formula in noncommutative geometry},
author = {Jyotishman Bhowmick and Debashish Goswami and Giovanni Landi},
journal= {arXiv preprint arXiv:1910.09306},
year = {2020}
}
Comments
To appear in Reviews in Mathematical Physics