Geodesic
On Some Classes of Bases in Finite-Dimensional Lie Algebras
Matematičeskie zametki, Tome 114 (2023) no. 2, pp. 203-211 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the paper, Lie algebras having bases of a special form (nice and beautiful bases) are considered. For nice bases, it is proved that, in a chosen nilpotent Lie algebra, their number (up to equivalence) is finite. For some Lie algebras of low dimension, it is shown that, when passing from a complex Lie algebra to its realification, the property to have a beautiful basis is lost.
Keywords: Lie algebra, nice basis
Mots-clés : equivalent bases. 
@article{MZM_2023_114_2_a3,
     author = {V. V. Gorbatsevich},
     title = {On {Some} {Classes} of {Bases} in {Finite-Dimensional} {Lie} {Algebras}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {203--211},
     year = {2023},
     volume = {114},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_114_2_a3/}
}
TY  - JOUR
AU  - V. V. Gorbatsevich
TI  - On Some Classes of Bases in Finite-Dimensional Lie Algebras
JO  - Matematičeskie zametki
PY  - 2023
SP  - 203
EP  - 211
VL  - 114
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MZM_2023_114_2_a3/
LA  - ru
ID  - MZM_2023_114_2_a3
ER  - 
%0 Journal Article
%A V. V. Gorbatsevich
%T On Some Classes of Bases in Finite-Dimensional Lie Algebras
%J Matematičeskie zametki
%D 2023
%P 203-211
%V 114
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_2023_114_2_a3/
%G ru
%F MZM_2023_114_2_a3
V. V. Gorbatsevich. On Some Classes of Bases in Finite-Dimensional Lie Algebras. Matematičeskie zametki, Tome 114 (2023) no. 2, pp. 203-211. http://geodesic.mathdoc.fr/item/MZM_2023_114_2_a3/

[1] J. Lauret, C. Will, “Einstein solvmanifolds: existence and non-existence questions”, Math. Ann., 350:1 (2011), 199–225 | DOI | MR

[2] D. Conti, F. A. Rossi, “Construction of nice nilpotent Lie groups”, J. Algebra, 525 (2019), 311–340 | DOI | MR

[3] E. B. Vinberg, V. V. Gorbatsevich, A. L. Onischik, “Stroenie grupp i algebr Li”, Gruppy Li i algebry Li – 3, Itogi nauki i tekhn. Ser. Sovrem. probl. mat. Fundam. napravleniya, 41, VINITI, M., 1990, 5–253 | MR | Zbl

[4] Dzh. Khamfri, Lineinye algebraicheskie gruppy, Nauka, M., 1980 | MR