Exterior differentials of higher order and their covariant generalization

Details Exterior differentials of higher order and their covariant generalization Exterior differentials of higher order and their covariant generalization

2000-04-26

arxiv.org/abs/math/0004162v1

Mathematics

Quantum Algebra

20 pages, no figures, to appear in J. Math. Phys

Scientific paper

10.1063/1.533428

We investigate a particular realization of generalized q-differential calculus of exterior forms on a smooth manifold based on the assumption that the N-th power (N>2) of exterior differential is equal to zero. 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 graded exterior calculus on a generalized Clifford algebra.

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