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

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.

14 pages

References in corpus (2)

• Tits type alternative for groups acting on toric affine varieties
• Algebraically generated groups and their lie algebras