Geodesic
The Growth of Varieties of Leibniz Algebras with Nilpotent Commutator Subalgebra
Matematičeskie zametki, Tome 82 (2007) no. 1, pp. 108-117.

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

It is proved that the exponents of certain varieties of Leibniz algebras with nilpotent commutator subalgebras exist and are integer.
Keywords: Leibniz algebra, growth of a variety, exponent of a variety, Young diagram, colength of a variety
Mots-clés : partition of an integer. 
@article{MZM_2007_82_1_a11,
     author = {S. M. Ratseev},
     title = {The {Growth} of {Varieties} of {Leibniz} {Algebras} with {Nilpotent} {Commutator} {Subalgebra}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {108--117},
     publisher = {mathdoc},
     volume = {82},
     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_1_a11/}
}
TY  - JOUR
AU  - S. M. Ratseev
TI  - The Growth of Varieties of Leibniz Algebras with Nilpotent Commutator Subalgebra
JO  - Matematičeskie zametki
PY  - 2007
SP  - 108
EP  - 117
VL  - 82
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2007_82_1_a11/
LA  - ru
ID  - MZM_2007_82_1_a11
ER  - 
%0 Journal Article
%A S. M. Ratseev
%T The Growth of Varieties of Leibniz Algebras with Nilpotent Commutator Subalgebra
%J Matematičeskie zametki
%D 2007
%P 108-117
%V 82
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2007_82_1_a11/
%G ru
%F MZM_2007_82_1_a11
S. M. Ratseev. The Growth of Varieties of Leibniz Algebras with Nilpotent Commutator Subalgebra. Matematičeskie zametki, Tome 82 (2007) no. 1, pp. 108-117. http://geodesic.mathdoc.fr/item/MZM_2007_82_1_a11/

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

[2] Yu. A. Bakhturin, Tozhdestva v algebrakh Li, Nauka, M., 1985 | MR | Zbl

[3] A. Giambruno, M. V. Zaicev, “On codimention growth of finitely generated associative algebras”, Adv. Math., 140:2 (1998), 145–155 | DOI | MR | Zbl

[4] M. V. Zaitcev, S. P. Mishchenko, “Example of variety of Lie algebras with fractional exponent”, J. Math. Sci. (N. Y.), 93:6 (1999), 977–982 | DOI | MR | Zbl

[5] S. P. Mischenko, “Nizhnie otsenki razmernostei neprivodimykh predstavlenii simmetricheskikh grupp i pokazatelei eksponenty mnogoobrazii algebr Li”, Matem. sb., 187:1 (1996), 83–94 | MR | Zbl

[6] S. P. Mishchenko, V. M. Petrogradsky, “Exponents of varieties of Lie algebras with a nilpotent commutator subalgebra”, Comm. Algebra, 27:5 (1999), 2223–2230 | DOI | MR | Zbl

[7] V. M. Petrogradskii, “O chislennykh kharakteristikakh podmnogoobrazii trekh mnogoobrazii algebr Li”, Matem. sb., 190:6 (1999), 111–126 | MR | Zbl

[8] S. P. Mischenko, “O mnogoobraziyakh polinomialnogo rosta algebr Li nad polem kharakteristiki nul”, Matem. zametki, 40:6 (1986), 713–721 | MR | Zbl

[9] V. M. Petrogradskii, “Rost polinilpotentnykh mnogoobrazii algebr Li i bystro rastuschie tselye funktsii”, Matem. sb., 188:6 (1997), 119–138 | MR | Zbl