On the third cohomology of the Lie algebra of vector fields on weighted densities on R
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929391073755136 |
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| author | Afsi, Wajd Omri, Salem |
| author_facet | Afsi, Wajd Omri, Salem |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12872 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the third cohomology of the Lie algebra of vector fields on weighted densities on R Afsi, Wajd Omri, Salem Rings and Algebras 17B56, 53D55, 58H15 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. |
| title | On the third cohomology of the Lie algebra of vector fields on weighted densities on R |
| topic | Rings and Algebras 17B56, 53D55, 58H15 |
| url | https://arxiv.org/abs/2406.12872 |