Geodesic
Classification of approximate Lie algebras with three essential vectors
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2010), pp. 3-17.

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

We propose an algorithm for classifying approximate Lie algebras whose bases are defined by essential vectors. We give a classification of Lie algebras with three essential vectors.
Keywords: Lie algebra, isomorphism of Lie algebras, transformations of basic vectors, essential vectors. 
@article{IVM_2010_10_a0,
     author = {R. K. Gazizov and V. O. Lukashchuk},
     title = {Classification of approximate {Lie} algebras with three essential vectors},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--17},
     publisher = {mathdoc},
     number = {10},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2010_10_a0/}
}
TY  - JOUR
AU  - R. K. Gazizov
AU  - V. O. Lukashchuk
TI  - Classification of approximate Lie algebras with three essential vectors
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2010
SP  - 3
EP  - 17
IS  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2010_10_a0/
LA  - ru
ID  - IVM_2010_10_a0
ER  - 
%0 Journal Article
%A R. K. Gazizov
%A V. O. Lukashchuk
%T Classification of approximate Lie algebras with three essential vectors
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2010
%P 3-17
%N 10
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2010_10_a0/
%G ru
%F IVM_2010_10_a0
R. K. Gazizov; V. O. Lukashchuk. Classification of approximate Lie algebras with three essential vectors. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2010), pp. 3-17. http://geodesic.mathdoc.fr/item/IVM_2010_10_a0/

[1] Baikov V. A., Gazizov R. K., Ibragimov N. Kh., “Priblizhennye gruppy preobrazovanii”, Differents. uravneniya, 29:10 (1993), 1712–1732 | MR

[2] Ibragimov N. H., CRC handbook of Lie group analysis of differential equations, v. 3, New trends in theoretical development and computational methods, CRC Press, FL, 1996 | MR | Zbl

[3] Mubarakzyanov G. M., “O razreshimykh algebrakh Li”, Izv. vuzov. Matematika, 1963, no. 1, 114–123 | MR | Zbl

[4] Mubarakzyanov G. M., “Klassifikatsiya veschestvennykh struktur algebr Li pyatogo poryadka”, Izv. vuzov. Matematika, 1963, no. 3, 99–106 | MR | Zbl

[5] Dzhekobson N., Algebry Li, Mir, M., 1964 | MR

[6] Petrov A. Z., Novye metody v obschei teorii otnositelnosti, Nauka, M., 1966 | MR

[7] Ovsyannikov L. V., Analiticheskie gruppy, Izd-vo NGU, Novosibirsk, 1972

[8] Gazizov R. K., Kovaleva (Lukaschuk) V. O., “Integrirovanie differentsialnykh uravnenii i sistem vtorogo poryadka s malym parametrom, imeyuschikh dve priblizhennye simmetrii”, Aktualnye problemy matematiki. Matem. modeli sovremennogo estestvoznaniya, Izd-vo UGATU, 2004, 68–76