Scalar curvature of a Levi-Civita connection on the Cuntz algebra with three generators

Abstract

A differential calculus on the Cuntz algebra with three generators coming from the action of rotation group in three dimensions is introduced. The differential calculus is shown to satisfy Assumptions I–IV of Bhowmick et al. (A new look at Levi-Civita Connection in NCG. arXiv:1606.08142) so that Levi-Civita connection exists uniquely for any pseudo-Riemannian metric in the sense of Bhowmick et al. [2] Scalar curvature is computed for the Levi-Civita connection corresponding to the canonical bilinear metric.