On finite-dimensional homogeneous Lie algebras of derivations of polynomial rings
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866908405329821696 |
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| author | Arzhantsev, Ivan Gaifullin, Sergey Lopatkin, Viktor |
| author_facet | Arzhantsev, Ivan Gaifullin, Sergey Lopatkin, Viktor |
| contents | For a finite set of homogeneous locally nilpotent derivations of the algebra of polynomials in several variables, a finite dimensionality criterion for the Lie algebra generated by these derivations is known. Also the structure of the corresponding finite-dimensional Lie algebras is described in previous works. In this paper, we obtain a finite dimensionality criterion for a Lie algebra generated by a finite set of homogeneous derivations, each of which is not locally nilpotent. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_05627 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On finite-dimensional homogeneous Lie algebras of derivations of polynomial rings Arzhantsev, Ivan Gaifullin, Sergey Lopatkin, Viktor Rings and Algebras Primary 17B05, 17B70, Secondary 17B40, 17B66 For a finite set of homogeneous locally nilpotent derivations of the algebra of polynomials in several variables, a finite dimensionality criterion for the Lie algebra generated by these derivations is known. Also the structure of the corresponding finite-dimensional Lie algebras is described in previous works. In this paper, we obtain a finite dimensionality criterion for a Lie algebra generated by a finite set of homogeneous derivations, each of which is not locally nilpotent. |
| title | On finite-dimensional homogeneous Lie algebras of derivations of polynomial rings |
| topic | Rings and Algebras Primary 17B05, 17B70, Secondary 17B40, 17B66 |
| url | https://arxiv.org/abs/2408.05627 |