connection

Geometry of quantum systems (e.g., noncommutative geometry and supergeometry) is mainly phrased in algebraic terms of modules and algebras. Connections on modules are generalization of a linear connection on a smooth vector bundle written as a Koszul connection on the -module of sections of . Commutative algebra Let be a commutative ring and an A-module. There are different equivalent definitions of a connection on . First definition