2000 character limit reached
On the Koszul formula in noncommutative geometry (1910.09306v2)
Published 21 Oct 2019 in math.QA, math-ph, and 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.