Journal of Lie Theory

no. 4
On Lie Algebras Consisting of Locally Nilpotent Derivations
Journal of Lie Theory, Volume 27 (2017) no. 4, pp. 1057-1068
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.
DOI: 10.5802/jolt.982
Classification: 17B66, 17B05, 13N15
Keywords: Lie algebra, vector field, triangular, locally nilpotent derivation 
@article{JOLT_2017_27_4_a8,
     author = {A. Petravchuk and K. Sysak},
     title = {On {Lie} {Algebras} {Consisting} of {Locally} {Nilpotent} {Derivations}},
     journal = {Journal of Lie Theory},
     pages = {1057--1068},
     year = {2017},
     volume = {27},
     number = {4},
     doi = {10.5802/jolt.982},
     zbl = {1430.17072},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.982/}
}
TY  - JOUR
AU  - A. Petravchuk
AU  - K. 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
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.982/
DO  - 10.5802/jolt.982
ID  - JOLT_2017_27_4_a8
ER  - 
%0 Journal Article
%A A. Petravchuk
%A K. Sysak
%T On Lie Algebras Consisting of Locally Nilpotent Derivations
%J Journal of Lie Theory
%D 2017
%P 1057-1068
%V 27
%N 4
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.982/
%R 10.5802/jolt.982
%F JOLT_2017_27_4_a8
A. Petravchuk; K. Sysak. On Lie Algebras Consisting of Locally Nilpotent Derivations. Journal of Lie Theory, Volume 27 (2017) no. 4, pp. 1057-1068. doi: 10.5802/jolt.982

Cited by Sources: