We propose a generalization of the concept of connection form by means of a graded q-differential algebra Ω q , 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 Ω q -connection on module and prove that every projective module admits an Ω q -connection. If the module is equipped with a Hermitian structure, we introduce a notion of an Ω q -connection consistent with the Hermitian structure.
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