×

zbMATH — the first resource for mathematics

Integral curves of derivations. (English) Zbl 0632.58017
A constructive method is presented for the integration of derivations of even degree on the sections of an exterior bundle by families of \({\mathbb{Z}}_ 2\)-graded algebra automorphisms. The method can be applied to the integration of superfields on graded manifolds.

MSC:
58C50 Analysis on supermanifolds or graded manifolds
17A70 Superalgebras
17A36 Automorphisms, derivations, other operators (nonassociative rings and algebras)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Batchelor, M., ?The structure of supermanifolds?, Trans. Amer. Math. Soc. 258 (1979), 329-338. · Zbl 0413.58002
[2] Bruzzo, U. & Cianci, R., ?Differential equations, Frobenius theorem and local flows on supermanifolds?, Phys. A: Math. Gen. 18 (1985), 417-423. · Zbl 0606.58040
[3] Fr?licher, A. & Nijenhuis, A., ?Theory of vector valued differential forms?, Part I. Indagationes Math. 18 (1956), 338-359. · Zbl 0079.37502
[4] Greub, W., Halperin, R. & Vanstone, R., ?Connections, curvature and cohomology?, Volume II, Pure and Applied Mathematics n? 47, Academic Press, New York, 1976. · Zbl 0372.57001
[5] Uhlmann, A., ?The Cartan algebra of exterior differential forms as a supermanifold: morphisms and manifolds associated with them?, JGP 1 (1984), 25-37. · Zbl 0587.58006
[6] Warner, F. W., ?Foundations of Differentiable Manifolds and Lie Groups?, Scott, Foresman and Co., Glenview, Ill., 1971. · Zbl 0241.58001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.