Let K be an algebraically closed field of characteristic zero and A an integral K-domain. The Lie algebra DerK(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 subalgebra of finite dimension (over K) of DerK(A) consisting of locally nilpotent derivations is nilpotent. In the case A = K[x, y], it is also proved that any subalgebra of DerK(A) consisting of locally nilpotent derivations is conjugate by an automorphism of K[x, y] with a subalgebra of the triangular Lie algebra.
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Dept. of Algebra and Mathematical Logic, Faculty of Mechanics and Mathematics, T. Shevchenko University, 64 Volodymyrska Street, Kyiv 01033, Ukraine
Anatoliy Petravchuk; Kateryna Sysak. On Lie Algebras Consisting of Locally Nilpotent Derivations. Journal of Lie Theory, Tome 27 (2017) no. 4, pp. 1057-1068. http://geodesic.mathdoc.fr/item/JOLT_2017_27_4_a8/
@article{JOLT_2017_27_4_a8,
author = {Anatoliy Petravchuk and Kateryna Sysak},
title = {On {Lie} {Algebras} {Consisting} of {Locally} {Nilpotent} {Derivations}},
journal = {Journal of Lie Theory},
pages = {1057--1068},
year = {2017},
volume = {27},
number = {4},
url = {http://geodesic.mathdoc.fr/item/JOLT_2017_27_4_a8/}
}
TY - JOUR
AU - Anatoliy Petravchuk
AU - Kateryna Sysak
TI - On Lie Algebras Consisting of Locally Nilpotent Derivations
JO - Journal of Lie Theory
PY - 2017
SP - 1057
EP - 1068
VL - 27
IS - 4
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