Abstract
We investigate the properties of differential algebras generated by an operator d satisfying the property d N = 0 instead of d 2 = 0 as in the usual case. The commutation relations for the generalized differentials ensuring the desired property can be put into the cyclic form a 1 a 2 a 3...a N = q a N a 1 a 2...a N−1, where q is a primitive N-th root of unity.
Examples of realizations of such differential algebras are given, either in the space of Z N-graded N × N matrix algebras, or as generalized differential calculus on manifolds. A generalization of gauge theories based on such differential calculus is briefly discussed.
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Kerner, R. Z n-graded differential calculus. Czechoslovak Journal of Physics 47, 33–40 (1997). https://doi.org/10.1023/A:1021487826985
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DOI: https://doi.org/10.1023/A:1021487826985