On Lie algebras consisting of locally nilpotent derivations

2016/08/04 by А. П. Петравчук, Petravchuk, A. P., K. Ya. Sysak +1
Mathematics · #Advanced Topics in Algebra #Finite Group Theory Research #Advanced Differential Equations and Dynamical Systems

paper · pdf · doi:10.48550/arxiv.1608.01490

Abstract

Let K be an algebraically closed field of characteristic zero and A an integral K-domain. The Lie algebra Der_K(A) of all K-derivations of A contains the set LND(A) of all locally nilpotent derivations. The structure of LND(A) is of great interest, and the question about properties of Lie algebras contained in LND(A) is still open. An answer to it in the finite dimensional case is given. It is proved that any finite dimensional (over K) subalgebra of Der_K(A) consisting of locally nilpotent derivations is nilpotent. In the case A=K[x, y], it is also proved that any subalgebra of Der_K(A) consisting of locally nilpotent derivations is conjugated by an automorphism of K[x, y] with a subalgebra of the triangular Lie algebra.

Related

• Locally nilpotent Lie algebras of derivations of integral domains
• Nilpotent Lie algebras of derivations with the center of small corank
• Local derivations on finite-dimensional Lie algebras
• Locally nilpotent sets of derivations
• Local derivations and automorphisms of nilpotent Lie algebra