Letters in Mathematical Physics

, Volume 109, Issue 12, pp 2665–2679 | Cite as

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

  • Soumalya JoardarEmail author


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.


Cuntz algebra Levi-Civita connection Scalar curvature 

Mathematics Subject Classification

46L87 58B34 



The author acknowledges support from Department of Science and Technology, India (DST/INSPIRE/04/2016/002469). He would like to thank J. Bhowmick for some fruitful discussions and both K. B. Sinha as well as Debashish Goswami for their words of encouragement. He would also like to thank an anonymous referee for his/her comments which helped in improving a previous version of the paper.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.IIT KanpurKalyanpur, KanpurIndia

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