Geodesic
The~Lie derivative and cohomology of $G$-structures
Lobachevskii journal of mathematics, Tome 3 (1999), pp. 197-200.

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - M. A. Malakhaltsev
TI  - The~Lie derivative and cohomology of $G$-structures
JO  - Lobachevskii journal of mathematics
PY  - 1999
SP  - 197
EP  - 200
VL  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/LJM_1999_3_a9/
LA  - en
ID  - LJM_1999_3_a9
ER  - 
%0 Journal Article
%A M. A. Malakhaltsev
%T The~Lie derivative and cohomology of $G$-structures
%J Lobachevskii journal of mathematics
%D 1999
%P 197-200
%V 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/LJM_1999_3_a9/
%G en
%F 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/