Geodesic
Naturally Graded Leibniz Algebras with Characteristic Sequence $(n-m, m)$
Matematičeskie zametki, Tome 93 (2013) no. 5, pp. 746-763 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider the classification problem for special classes of nilpotent Leibniz algebras. Namely, we consider “naturally” graded nilpotent $n$-dimensional Leibniz algebras for which the right multiplication operator (by the generic element) has two Jordan blocks of dimensions $m$ and $n-m$. Earlier, the problem of classifying such algebras was studied for $m<4$. The present paper continues these studies for the case $m\ge4$.
Keywords: nilpotent Leibniz algebra, naturally graded Leibniz algebra, right multiplication operator, Lie algebra, nil-filiform Leibniz algebra, Jordan block, lower central series, nilpotency index, nil-index. 
@article{MZM_2013_93_5_a9,
     author = {K. K. Masutova and B. A. Omirov and A. Kh. Khudojberdyjev},
     title = {Naturally {Graded} {Leibniz} {Algebras} with {Characteristic} {Sequence} $(n-m, m)$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {746--763},
     year = {2013},
     volume = {93},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_93_5_a9/}
}
TY  - JOUR
AU  - K. K. Masutova
AU  - B. A. Omirov
AU  - A. Kh. Khudojberdyjev
TI  - Naturally Graded Leibniz Algebras with Characteristic Sequence $(n-m, m)$
JO  - Matematičeskie zametki
PY  - 2013
SP  - 746
EP  - 763
VL  - 93
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/MZM_2013_93_5_a9/
LA  - ru
ID  - MZM_2013_93_5_a9
ER  - 
%0 Journal Article
%A K. K. Masutova
%A B. A. Omirov
%A A. Kh. Khudojberdyjev
%T Naturally Graded Leibniz Algebras with Characteristic Sequence $(n-m, m)$
%J Matematičeskie zametki
%D 2013
%P 746-763
%V 93
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_2013_93_5_a9/
%G ru
%F MZM_2013_93_5_a9
K. K. Masutova; B. A. Omirov; A. Kh. Khudojberdyjev. Naturally Graded Leibniz Algebras with Characteristic Sequence $(n-m, m)$. Matematičeskie zametki, Tome 93 (2013) no. 5, pp. 746-763. http://geodesic.mathdoc.fr/item/MZM_2013_93_5_a9/

[1] J. L. Loday, “Une version non commutative des algèbres de Lie: les algèbres de Leibniz”, Enseign. Math. (2), 39:3-4 (1993), 269–293 | MR | Zbl

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

[3] A. I. Maltsev, “O razreshimykh algebrakh Li”, Izv. AN SSSR. Ser. matem., 9:5 (1945), 329–356 | MR | Zbl

[4] J. R. Gómez, A. Jiménez-Merchán, “Naturally graded quasi-filiform Lie algebras”, J. Algebra, 256:1 (2002), 211–228 | DOI | MR | Zbl

[5] J. R. Gómez, A. Jiménez-Merchán, J. Reyes, “Maximum length filiform Lie algebras”, Exstracta Math., 16:3 (2001), 405–421 | MR | Zbl

[6] M. Goze, Y. Khakimdjanov, Nilpotent Lie Algebras, Math. Appl., 361, Kluwer Academic Publ., Dordrecht, 1996 | MR | Zbl

[7] Sh. A. Ayupov, B. A. Omirov, “O nekotorykh klassakh nilpotentnykh algebr Leibnitsa”, Sib. matem. zhurn., 42:1 (2001), 18–29 | MR | Zbl

[8] Sh. A. Ayupov, B. A. Omirov, “On Leibniz qlgebras”, Algebra and Operators Theory (Tashkent, 1997), Kluwer Academic Publ., Dordrecht, 1998, 1–12 | MR | Zbl

[9] L. M. Camacho, J. R. Gómez, A. R. González, B. A. Omirov, “Naturally graded quasi-filiform Leibniz algebras”, J. Symbolic Comput., 44:5 (2009), 527–539 | DOI | MR | Zbl

[10] L. M. Camacho, J. R. Gómez, A. J. González, B. A. Omirov, “The classification of naturally graded $p$-filiform Leibniz algebras”, Comm. Algebra, 39:1 (2011), 153–168 | MR | Zbl

[11] A. O. Gelfond, Ischislenie konechnykh raznostei, Nauka, M., 1967 | MR | Zbl

[12] J. M. Cabezas, L. M. Camacho, J. R. Gómez, B. A. Omirov, “A class of Leibniz algebras in arbitrary finite dimension”, 2010 (to appear)