Derivations of Lie Algebras of Vector Fields in Infinitely Many Variables
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866913929592045568 |
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| author | Bezushchak, Oksana Kashuba, Iryna |
| author_facet | Bezushchak, Oksana Kashuba, Iryna |
| contents | Let $W_X(\mathbb{F})$ be the Lie algebra of all derivations of the polynomial algebra $\mathbb{F}[X]$ in infinitely many variables. We describe all derivations of $W_X(\mathbb{F})$ over a field of characteristic zero and prove that all such derivations are inner. We also consider the subalgebras $W_\infty(\mathbb{F})$ and $W_{\text{fin}}(\mathbb{F})$ of the algebra $W_X(\mathbb{F})$ and describe all of their derivations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04541 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Derivations of Lie Algebras of Vector Fields in Infinitely Many Variables Bezushchak, Oksana Kashuba, Iryna Rings and Algebras Primary 16W25, 17B66, Secondary 17A36, 17B40, 17B56 Let $W_X(\mathbb{F})$ be the Lie algebra of all derivations of the polynomial algebra $\mathbb{F}[X]$ in infinitely many variables. We describe all derivations of $W_X(\mathbb{F})$ over a field of characteristic zero and prove that all such derivations are inner. We also consider the subalgebras $W_\infty(\mathbb{F})$ and $W_{\text{fin}}(\mathbb{F})$ of the algebra $W_X(\mathbb{F})$ and describe all of their derivations. |
| title | Derivations of Lie Algebras of Vector Fields in Infinitely Many Variables |
| topic | Rings and Algebras Primary 16W25, 17B66, Secondary 17A36, 17B40, 17B56 |
| url | https://arxiv.org/abs/2507.04541 |