Differential Calculus on N-Graded Manifolds

Autor: G. Sardanashvily, W. Wachowski
Jazyk: angličtina
Rok vydání: 2017
Předmět:
Zdroj: Journal of Mathematics, Vol 2017 (2017)
Druh dokumentu: article
ISSN: 2314-4629
2314-4785
97144444
DOI: 10.1155/2017/8271562
Popis: The differential calculus, including formalism of linear differential operators and the Chevalley–Eilenberg differential calculus, over N-graded commutative rings and on N-graded manifolds is developed. This is a straightforward generalization of the conventional differential calculus over commutative rings and also is the case of the differential calculus over Grassmann algebras and on Z2-graded manifolds. We follow the notion of an N-graded manifold as a local-ringed space whose body is a smooth manifold Z. A key point is that the graded derivation module of the structure ring of graded functions on an N-graded manifold is the structure ring of global sections of a certain smooth vector bundle over its body Z. Accordingly, the Chevalley–Eilenberg differential calculus on an N-graded manifold provides it with the de Rham complex of graded differential forms. This fact enables us to extend the differential calculus on N-graded manifolds to formalism of nonlinear differential operators, by analogy with that on smooth manifolds, in terms of graded jet manifolds of N-graded bundles.
Databáze: Directory of Open Access Journals
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