Geodesic
On Some Classes of Bases in Finite-Dimensional Lie Algebras
Matematičeskie zametki, Tome 114 (2023) no. 2, pp. 203-211

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
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     author = {V. V. Gorbatsevich},
     title = {On {Some} {Classes} of {Bases} in {Finite-Dimensional} {Lie} {Algebras}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {203--211},
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     year = {2023},
     language = {ru},
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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/