Scalar Curvature of a Levi-Civita Connection on Cuntz algebra with three generators

Abstract: A differential calculus on 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 [1] so that Levi-Civita Connection exists uniquely for any pseudo-Riemannian metric in the sense of [1]. Scalar curvature is computed for the Levi-Civita connection corresponding to the canonical bilinear metric.