Michel Dubois-Violette, Peter W. Michor
Connections on Central Bimodules
The paper is published: J. Geom. Physics 20 (1996) 218-230

MSC:

53C05 Connections, general theory

58B30 Noncommutative differential geometry and topology, See also {46L30, 46L87, 46L89}

16W25 Derivations, actions of Lie algebras

53B15 Other connections

46L87 Noncommutative differential geometry, See also {58B30,

16S32 Rings of differential operators, See also {13N10, 32C38}

16D20 Bimodules

Abstract: We define and study the theory of derivation-based connections on a
recently introduced class of bimodules over an algebra which reduces
to the category of modules whenever the algebra is commutative. This
theory contains, in particular, a noncommutative generalization of
linear connections. We also discuss the different noncommutative versions
of differential forms based on derivations. Then we investigate reality
conditions and a noncommutative generalization of
pseudo-riemannian structures.

Keywords: central bimodule, connection