The~Lie derivative and cohomology of $G$-structures
Lobachevskii journal of mathematics, Tome 3 (1999), pp. 197-200
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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].
@article{LJM_1999_3_a9,
author = {M. A. Malakhaltsev},
title = {The~Lie derivative and cohomology of $G$-structures},
journal = {Lobachevskii journal of mathematics},
pages = {197--200},
publisher = {mathdoc},
volume = {3},
year = {1999},
language = {en},
url = {http://geodesic.mathdoc.fr/item/LJM_1999_3_a9/}
}
M. A. Malakhaltsev. The~Lie derivative and cohomology of $G$-structures. Lobachevskii journal of mathematics, Tome 3 (1999), pp. 197-200. http://geodesic.mathdoc.fr/item/LJM_1999_3_a9/