Generalization of connection based on the concept of gradedq-differential algebra

Abstract

We propose a generalization of the concept of connection form by means of a graded q-differential algebra Wq, where q is a primitive Nth root of unity, and develop the concept of curvature N-form for this generalization of the connection form. The Bianchi identity for a curvature N-form is proved. We study an Wq-connection on module and prove that every projective module admits an Wq-connection. If the module is equipped with a Hermitian structure, we introduce a notion of an Wq-connection consistent with the Hermitian structure.