International Journal of Mathematics ( IF 0.604 ) Pub Date : 2020-06-23 , DOI: 10.1142/s0129167x20500652 Jyotishman Bhowmick; Debashish Goswami; Giovanni Landi
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.