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arXiv · 2408.05627

On finite-dimensional homogeneous Lie algebras of derivations of polynomial rings

Ivan Arzhantsev·Sergey Gaifullin·Viktor Lopatkin
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Abstract

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.

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Ivan Arzhantsev, Sergey Gaifullin, Viktor Lopatkin. 2024-08-10. On finite-dimensional homogeneous Lie algebras of derivations of polynomial rings. https://doi.org/10.4213/im9615e

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