Geodesic
Condition of finiteness of colength of variety of Leibnitz algebras
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 10 (2014), pp. 84-90

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

This paper is devoted to the varieties of Leibnitz algebras over a field of zero characteristic. All information about the variety in case of zero characteristic of the base field is contained in the space of multilinear elements of its relatively free algebra. Multilinear component of variety is considered as a module of symmetric group and splits into a direct sum of irreducible submodules, the sum of multiplicities of which is called colength of variety. This paper investigates the identities that are performed in varieties with finite colength and also the relationship of this varieties with known varieties of Lie and Leibnitz algebras with this property. We prove necessary and sufficient condition for a finiteness of colength of variety of Leibnitz algebras.
Keywords: linear algebra, Leibnitz algebra, Lie algebra, variety of algebras, multilinear part of variety, Yung diagrams, numerical characteristics of variety, colength of variety. 
@article{VSGU_2014_10_a8,
     author = {A. V. Polovinkina and T. V. Skoraya},
     title = {Condition of finiteness of colength of variety of {Leibnitz} algebras},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {84--90},
     publisher = {mathdoc},
     number = {10},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2014_10_a8/}
}
TY  - JOUR
AU  - A. V. Polovinkina
AU  - T. V. Skoraya
TI  - Condition of finiteness of colength of variety of Leibnitz algebras
JO  - Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
PY  - 2014
SP  - 84
EP  - 90
IS  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSGU_2014_10_a8/
LA  - ru
ID  - VSGU_2014_10_a8
ER  - 
%0 Journal Article
%A A. V. Polovinkina
%A T. V. Skoraya
%T Condition of finiteness of colength of variety of Leibnitz algebras
%J Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
%D 2014
%P 84-90
%N 10
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSGU_2014_10_a8/
%G ru
%F VSGU_2014_10_a8
A. V. Polovinkina; T. V. Skoraya. Condition of finiteness of colength of variety of Leibnitz algebras. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 10 (2014), pp. 84-90. http://geodesic.mathdoc.fr/item/VSGU_2014_10_a8/