Geodesic
Maximal Lie subalgebras among locally nilpotent derivations
Sbornik. Mathematics, Tome 212 (2021) no. 2, pp. 265-271 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study maximal Lie subalgebras among locally nilpotent derivations of the polynomial algebra. Freudenburg conjectured that the triangular Lie algebra of locally nilpotent derivations of the polynomial algebra is a maximal Lie algebra contained in the set of locally nilpotent derivations, and that every maximal Lie algebra contained in the set of locally nilpotent derivations is conjugate to the triangular Lie algebra. In this paper we prove the first part of the conjecture and present a counterexample to the second part. We also show that under a certain natural condition imposed on a maximal Lie algebra there is a conjugation taking this Lie algebra to the triangular Lie algebra. Bibliography: 2 titles.
Keywords: Lie algebra, locally nilpotent derivation.
Mots-clés : polynomial algebra 
@article{SM_2021_212_2_a5,
     author = {A. A. Skutin},
     title = {Maximal {Lie} subalgebras among locally nilpotent derivations},
     journal = {Sbornik. Mathematics},
     pages = {265--271},
     year = {2021},
     volume = {212},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2021_212_2_a5/}
}
TY  - JOUR
AU  - A. A. Skutin
TI  - Maximal Lie subalgebras among locally nilpotent derivations
JO  - Sbornik. Mathematics
PY  - 2021
SP  - 265
EP  - 271
VL  - 212
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_2021_212_2_a5/
LA  - en
ID  - SM_2021_212_2_a5
ER  - 
%0 Journal Article
%A A. A. Skutin
%T Maximal Lie subalgebras among locally nilpotent derivations
%J Sbornik. Mathematics
%D 2021
%P 265-271
%V 212
%N 2
%U http://geodesic.mathdoc.fr/item/SM_2021_212_2_a5/
%G en
%F SM_2021_212_2_a5
A. A. Skutin. Maximal Lie subalgebras among locally nilpotent derivations. Sbornik. Mathematics, Tome 212 (2021) no. 2, pp. 265-271. http://geodesic.mathdoc.fr/item/SM_2021_212_2_a5/

[1] G. Freudenburg, Algebraic theory of locally nilpotent derivations, Encyclopaedia Math. Sci., 136, Invariant Theory Algebr. Transform. Groups, VII, Springer-Verlag, Berlin, 2006, xii+261 pp. | DOI | MR | Zbl

[2] D. Daigle, “A necessary and sufficient condition for triangulability of derivations of $k[X, Y, Z]$”, J. Pure Appl. Algebra, 113:3 (1996), 297–305 | DOI | MR | Zbl