
Journal of Lie Theory 27 (2017), No. 4, 10571068 Copyright Heldermann Verlag 2017 On Lie Algebras Consisting of Locally Nilpotent Derivations Anatoliy Petravchuk Dept. of Algebra and Mathematical Logic, Faculty of Mechanics and Mathematics, T. Shevchenko University, 64 Volodymyrska Street, Kyiv 01033, Ukraine aptr@univ.kiev.ua Kateryna Sysak Dept. of Algebra and Mathematical Logic, Faculty of Mechanics and Mathematics, T. Shevchenko University, 64 Volodymyrska Street, Kyiv 01033, Ukraine sysakkya@gmail.com Let K be an algebraically closed field of characteristic zero and A an integral Kdomain. The Lie algebra Der_{K}(A) of all Kderivations 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 subalgebra of finite dimension (over K) 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 conjugate by an automorphism of K[x, y] with a subalgebra of the triangular Lie algebra. Keywords: Lie algebra, vector field, triangular, locally nilpotent derivation. MSC: 17B66, 17B05, 13N15 [ Fulltextpdf (279 KB)] for subscribers only. 