Title

Levi-Civita connections and vector fields for noncommutative differential calculi

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

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