Geodesic
Prolongations of Vector Fields on Lie Groups and Homogeneous Spaces
Teoretičeskaâ i matematičeskaâ fizika, Tome 135 (2003) no. 1, pp. 70-81

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We introduce the notion of the $\mathfrak{gl}(V)$-prolongation of Lie algebras of differential operators on homogeneous spaces. The $\mathfrak{gl}(V)$-prolongations are topological invariants that coincide with one-dimensional cohomologies of the corresponding Lie algebras in the case where $V$ is a homogeneous space. We apply the obtained results to the spaces $S^1$ (the Virasoro algebra) and $\mathbb R^1$.
Keywords: Lie groups, homogeneous spaces, vector fields
Mots-clés : Lie algebra cohomologies. 
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     author = {S. P. Baranovskii and I. V. Shirokov},
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S. P. Baranovskii; I. V. Shirokov. Prolongations of Vector Fields on Lie Groups and Homogeneous Spaces. Teoretičeskaâ i matematičeskaâ fizika, Tome 135 (2003) no. 1, pp. 70-81. http://geodesic.mathdoc.fr/item/TMF_2003_135_1_a2/