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

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Abstract

For a finite set of homogeneous locally nilpotent derivations of the algebraof polynomials in several variables, a finite dimensionality criterionfor the Lie algebra generated by these derivations is known.The structure of the corresponding finite-dimensional Lie algebraswas also described in previous works. In this paper, we obtaina finite dimensionality criterion for a Lie algebra generated by a finite setof homogeneous derivations, each of which is not locally nilpotent.

About the authors

Ivan Vladimirovich Arzhantsev

National Research University Higher School of Economics, Moscow

Author for correspondence.
Email: arjantsev@hse.ru
Doctor of physico-mathematical sciences, Professor

Sergey Aleksandrovich Gaifullin

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics; Moscow Center for Fundamental and Applied Mathematics; National Research University Higher School of Economics, Moscow

Email: sgayf@yandex.ru
Candidate of physico-mathematical sciences

Viktor Evgenyavich Lopatkin

National Research University Higher School of Economics, Moscow

Email: Wickktor@gmail.com
Candidate of physico-mathematical sciences, no status

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