Linear connections on almost commutative algebras. (English) Zbl 1087.81032

Ciupală, C.

Acta Math. Univ. Comen., New Ser. 72, No. 2, 197-206 (2003).

Summary: In this paper we study a linear connection on bimodules over almost commutative algebras using the framework of noncommutative geometry. We also present its curvature and its torsion. As an example there are presented linear connections on \(N\)-dimensional quantum hyperplane over two kinds of bimodules.

MSC:

81R60	Noncommutative geometry in quantum theory
16W99	Associative rings and algebras with additional structure
53B05	Linear and affine connections

Keywords:

noncommutative geometry; quantum hyperplane; linear connections