ON REALIZATIONS OF EXTERIOR CALCULUS WITH dN = 0*)

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Abstract

We study realizations of the q-exterior calculus with exterior differential d satisfying dN = 0, N > 2 on the free associative algebra with one generator and on the generalized Clifford algebras. Analogs of the notions of connection and curvature are discussed in the case of the q-exterior calculus on the generalized Clifford algebra. We show that the q-exterior calculus on the free associative algebra with one generator is related to q-calculus on the braided line.

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