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arXiv · 2406.12872

On the third cohomology of the Lie algebra of vector fields on weighted densities on R

Wajd Afsi·Salem Omri
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Abstract

Let Vect($\mathbb{R}$) be the Lie algebra of smooth vector fields on $\mathbb{R}$ and $\mathbb{F}_λ$ be the space of $λ$-densities on $\mathbb{R}$. Vect($\mathbb{R}$) acts on $\mathbb{F}_λ$ by Lie derivative. In this paper, we compute the third differential cohomology of the Lie algebra Vect($\mathbb{R}$) with coeffcients in the space $\mathbb{F}_λ.$ Explicit cocycles spanning these cohomology spaces are given.

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Wajd Afsi, Salem Omri. 2024-04-28. On the third cohomology of the Lie algebra of vector fields on weighted densities on R. https://arxiv.org/abs/2406.12872

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