Levi-Civita connections and vector fields for noncommutative differential calculi

Authors

Jyotishman Bhowmick, Indian Statistical Institute, Kolkata
Debashish Goswami, Indian Statistical Institute, Kolkata
Giovanni Landi, Università degli Studi di Trieste

Article Type

Research Article

Publication Title

International Journal of Mathematics

Abstract

We study covariant derivatives on a class of centered bimodules over an algebra . We begin by identifying a ()-submodule () which can be viewed as the analogue of vector fields in this context; () is proven to be a Lie algebra. Connections on are in one-to-one correspondence with covariant derivatives on (). We recover the classical formulas of torsion and metric compatibility of a connection in the covariant derivative form. As a result, a Koszul formula for the Levi-Civita connection is also derived.

DOI

10.1142/S0129167X20500652

Publication Date

7-1-2020

Comments

Open Access, Green

Recommended Citation

Bhowmick, Jyotishman; Goswami, Debashish; and Landi, Giovanni, "Levi-Civita connections and vector fields for noncommutative differential calculi" (2020). Journal Articles. 205.
https://digitalcommons.isical.ac.in/journal-articles/205