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Lobachevskii Journal of Mathematics, 1999, Volume 3, Pages 197–200 (Mi ljm167)  

This article is cited in 1 scientific paper (total in 1 paper)

The Lie derivative and cohomology of $G$-structures

M. A. Malakhaltsev

Kazan State University
Full-text PDF (100 kB) Citations (1)
Abstract: In [1], J. F. Pommaret constructed the so-called Spencer $P$-complex for a differential operator. Applying this construction to the Lie derivative associated with a general pseudogroup structure on a smooth manifold, he defined the deformation cohomology of a pseudogroup structure. The aim of this paper is to specify this complex for a particular case of pseudogroup structure, namely, for a first-order $G$-structure, and to express this complex in differential geometric form, i.e., in terms of tensor fields and the covariant derivative. We show that the Pommaret construction provides a powerful tool for associating a differential complex to a $G$-structure. In a unified way one can obtain the Dolbeaut complex for the complex structure, the Vaisman complex for the foliation structure [2], and the Vaisman–Molino cohomology for the structure of manifold over an algebra [3].
Submitted by: B. N. Shapukov
Received: 27.07.1999
Bibliographic databases:
Language: English
Citation: M. A. Malakhaltsev, “The Lie derivative and cohomology of $G$-structures”, Lobachevskii J. Math., 3 (1999), 197–200
Citation in format AMSBIB
\Bibitem{Mal99}
\by M.~A.~Malakhaltsev
\paper The~Lie derivative and cohomology of $G$-structures
\jour Lobachevskii J. Math.
\yr 1999
\vol 3
\pages 197--200
\mathnet{http://mi.mathnet.ru/ljm167}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1743138}
\zmath{https://zbmath.org/?q=an:0958.58019}
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  • This publication is cited in the following 1 articles:
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