EAP - Proceedings of the Estonian Academy of Sciences

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proceedings
of the estonian academy of sciences

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Generalization of connection based on the concept of graded q-differential algebra; pp. 256–264

PDF | doi: 10.3176/proc.2010.4.02

Authors

Viktor Abramov, Olga Liivapuu

Abstract

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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