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.

arXiv comment14 pages

References in corpus (6)

• Affine T-varieties of complexity one and locally nilpotent derivations
• Ga-actions of fiber type on affine T-varieties
• On the geometry of the automorphism groups of affine varieties
• Tits type alternative for groups acting on toric affine varieties
• Lie algebras of vertical derivations on semiaffine varieties with torus actions
• Algebraically generated groups and their lie algebras