Abstract
We introduce the notion of the \({\mathfrak{g}}{\mathfrak{l}(V)}\)-prolongation of Lie algebras of differential operators on homogeneous spaces. The \({\mathfrak{g}}{\mathfrak{l}(V)}\)-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 \({\mathbb{R}}^1 \).
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Baranovskii, S., Shirokov, I. Prolongations of Vector Fields on Lie Groups and Homogeneous Spaces. Theoretical and Mathematical Physics 135, 510–519 (2003). https://doi.org/10.1023/A:1023283418983
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DOI: https://doi.org/10.1023/A:1023283418983