Geodesic
On liezation of the Leibniz algebras and its applications
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2016), pp. 14-22.

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

We consider some the fundamental properties of the Leibniz algebras. Some results were known before, but in the paper they are proved by a single method of liezation – the transition to a Lie algebra, which gives for a number of cases greatly simplified proof. There are also some new results.
Keywords: Leibniz algebra, Lie algebra. 
@article{IVM_2016_4_a2,
     author = {V. V. Gorbatsevich},
     title = {On liezation of the {Leibniz} algebras and its applications},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {14--22},
     publisher = {mathdoc},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_4_a2/}
}
TY  - JOUR
AU  - V. V. Gorbatsevich
TI  - On liezation of the Leibniz algebras and its applications
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2016
SP  - 14
EP  - 22
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2016_4_a2/
LA  - ru
ID  - IVM_2016_4_a2
ER  - 
%0 Journal Article
%A V. V. Gorbatsevich
%T On liezation of the Leibniz algebras and its applications
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2016
%P 14-22
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2016_4_a2/
%G ru
%F IVM_2016_4_a2
V. V. Gorbatsevich. On liezation of the Leibniz algebras and its applications. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2016), pp. 14-22. http://geodesic.mathdoc.fr/item/IVM_2016_4_a2/

[1] Blokh A. M., “Ob odnom obobschenii ponyatiya algebry Li”, DAN SSSR, 165 (1965), 471–473 | Zbl

[2] Blokh A. M., “Teoriya gomologii Kartana–Eilenberga dlya odnogo obobscheniya klassa algebr Li”, DAN SSSR, 175 (1967), 266–268 | Zbl

[3] Loday J.-L., “Une version non commutative des algèbres de Lie: les algèbres de Leibniz”, Enseign. Math. II Sér., 39:3–4 (1993), 269–293 | MR | Zbl

[4] Zinbiel G. W., “Encyclopedia of types of algebras 2010”: Bai C., Guo L., Loday J.-L., Operads and universal algebra, Proceedings of the Summer School and International Conference (Tianjin, China, July 5–9, 2010), Nankai Series in Pure, Appl. Math. and Theor.Phys., 9, World Scientific, Hackensack, NJ, 2012, 217–298 | MR

[5] Ayupov Sh., Omirov B., “On Leibniz algebras”, Algebra and Operator Theory, Proc. of the colloquium in Tashkent, Kluwer Acad. Publ., Dordrecht–Boston–London, 1997, 1–13 | MR

[6] Patsourakos A., “On nilpotent properties of Leibniz algebras”, Commun. Algebra, 35 (2007), 3828–3834 | DOI | MR | Zbl

[7] Burbaki N., Gruppy i algebry Li, gl. I–III, Mir, M., 1976 | MR

[8] Albeverio S., Ayupov Sh., Omirov B., “Cartan subalgebras and criterion of solvability of finite dimensional Leibniz algebras”, Revista Matem. Complutense, 19 (2006), 183–195 | MR | Zbl

[9] Barnes D., “On Levi's theorem for Leibniz algebras”, Bull. Austral. Math. Soc., 86 (2012), 184–185 | DOI | MR | Zbl