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 -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