2 00 0 Exterior Differentials of Higher Order and Their Covariant
نویسنده
چکیده
We investigate a particular realization of generalized q-differential calculus of exterior forms on a smooth manifold based on the assumption that d N = 0 while d k = 0 for k < N. It implies the existence of cyclic commutation relations for the differentials of first order and their generalization for the differentials of higher order. Special attention is paid to the cases N = 3 and N = 4. A covariant basis of the algebra of such q-grade forms is introduced, and the analogues of torsion and curvature of higher order are considered. We also study a Z N-graded exterior calculus on a generalized Clifford algebra.
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