Work

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

Year: 2025

Type: article

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. The structure of the corresponding finite-dimensional Lie algebras was also 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.

Source: Izvestiya Mathematics

DOI: 10.4213/im9615e

Authors: Ivan Arzhantsev, Sergey Aleksandrovich Gaifullin, Viktor Evgenyavich Lopatkin

Institutions: National Research University Higher School of Economics, Lomonosov Moscow State University, Moscow Center of Fundamental and Applied Mathematics

Language: English

Topic: Advanced Topics in Algebra

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

OpenAlex ID: W4411208816

FWCI:

Cites: 26

Cited by:

Related to: 10