English

Levi-Civita connections from toral actions

Quantum Algebra 2022-09-14 v3 Operator Algebras

Abstract

We construct tame differential calculi coming from toral actions on a class of C\mathrm{C}^*-algebras. Relying on the existence of a unique Levi-Civita connection on such a calculus, we prove a version of the Bianchi identity. A Gauss-Bonnet theorem for the canonical tame calculus of rank two is studied.

Keywords

Cite

@article{arxiv.2104.07570,
  title  = {Levi-Civita connections from toral actions},
  author = {Suvrajit Bhattacharjee and Soumalya Joardar and Sugato Mukhopadhyay},
  journal= {arXiv preprint arXiv:2104.07570},
  year   = {2022}
}

Comments

Revised version following the referee's suggestions. To appear in Journal of Geometry and Physics