Geodesic
Lie Algebras with Abelian Centralizers
Matematičeskie zametki, Tome 101 (2017) no. 5, pp. 690-699.

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

In the paper, finite-dimensional real Lie algebras for which the centralizers of all nonzero element are Abelian are studied. These Lie algebras are also characterized by the transitivity condition for the commutation relation for two nonzero elements. A complete description of these Lie algebras up to isomorphism is given. Some results concerning the relationship between the aforementioned Lie algebras and the Lie algebras of vector fields whose orbits are one-dimensional are considered.
Keywords: Lie algebra, centralizer, CT Lie algebra, Lie algebra of vector fields. 
@article{MZM_2017_101_5_a4,
     author = {V. V. Gorbatsevich},
     title = {Lie {Algebras} with {Abelian} {Centralizers}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {690--699},
     publisher = {mathdoc},
     volume = {101},
     number = {5},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_101_5_a4/}
}
TY  - JOUR
AU  - V. V. Gorbatsevich
TI  - Lie Algebras with Abelian Centralizers
JO  - Matematičeskie zametki
PY  - 2017
SP  - 690
EP  - 699
VL  - 101
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2017_101_5_a4/
LA  - ru
ID  - MZM_2017_101_5_a4
ER  - 
%0 Journal Article
%A V. V. Gorbatsevich
%T Lie Algebras with Abelian Centralizers
%J Matematičeskie zametki
%D 2017
%P 690-699
%V 101
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2017_101_5_a4/
%G ru
%F MZM_2017_101_5_a4
V. V. Gorbatsevich. Lie Algebras with Abelian Centralizers. Matematičeskie zametki, Tome 101 (2017) no. 5, pp. 690-699. http://geodesic.mathdoc.fr/item/MZM_2017_101_5_a4/

[1] I. Klep, P. Moravec, “Lie algebras with abelian centralizers”, Algebra Colloq., 17:4 (2010), 629–636 | DOI | MR | Zbl

[2] I. V. Arzhantsev, E. A. Makedonskii, A. P. Petravchuk, “Finite-dimensional subalgebras in polynomial Lie algebras of rank one”, Ukr. matem. zhurn., 63:5 (2011), 708–712 | MR | Zbl

[3] M. Suzuki, “The nonexistence of a certain type of simple groups of odd order”, Proc. Amer. Math. Soc., 8 (1957), 686–695 | DOI | MR | Zbl

[4] R. Khorn, Ch. Dzhonson, Matrichnyi analiz, Mir, M., 1989 | MR | Zbl

[5] I. M. Gelfand, V. A. Ponomarev, “Zamechaniya o klassifikatsii pary kommutiruyuschikh lineinykh preobrazovanii v konechnomernom prostranstve”, Funkts. analiz i ego pril., 3:4 (1969), 81–82 | MR | Zbl

[6] S. Li, Simmetrii differentsialnykh uravnenii. Lektsii o differentsialnykh uravneniyakh s izvestnymi infinitezimalnymi preobrazovaniyami, Tom 1, NITs Regulyarnaya i khaoticheskaya dinamika, M.–Izhevsk, 2011