Basis of multilinear part of Leibniz algebras manifolds $\widetilde{\mathrm{V}}_1$
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 3 (2014), pp. 76-82 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the case of trivial characteristic of base field, Leibniz algebras manifolds defined by the identity $x_1(x_2x_3)(x_4x_5)\equiv0$, has almost polynomial growth. In the work we continue research of this manifold, in particular, we construct bases of multilinear parts.
Keywords: Leibniz algebra, manifold, almost polynomial growth, bases of multilinear part.
@article{VSGU_2014_3_a7,
     author = {S. P. Mishchenko and Y. R. Pestova},
     title = {Basis of multilinear part of {Leibniz} algebras manifolds~$\widetilde{\mathrm{V}}_1$},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {76--82},
     year = {2014},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2014_3_a7/}
}
TY  - JOUR
AU  - S. P. Mishchenko
AU  - Y. R. Pestova
TI  - Basis of multilinear part of Leibniz algebras manifolds $\widetilde{\mathrm{V}}_1$
JO  - Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
PY  - 2014
SP  - 76
EP  - 82
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VSGU_2014_3_a7/
LA  - ru
ID  - VSGU_2014_3_a7
ER  - 
%0 Journal Article
%A S. P. Mishchenko
%A Y. R. Pestova
%T Basis of multilinear part of Leibniz algebras manifolds $\widetilde{\mathrm{V}}_1$
%J Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
%D 2014
%P 76-82
%N 3
%U http://geodesic.mathdoc.fr/item/VSGU_2014_3_a7/
%G ru
%F VSGU_2014_3_a7
S. P. Mishchenko; Y. R. Pestova. Basis of multilinear part of Leibniz algebras manifolds $\widetilde{\mathrm{V}}_1$. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 3 (2014), pp. 76-82. http://geodesic.mathdoc.fr/item/VSGU_2014_3_a7/

[1] Giambruno A., Zaicev M., Polynomial Identities and Asymptotic Methods, Mathematical Surveys and Monographs, 122, AMS, Providence, RI, 2005, 344 pp. | DOI | MR | Zbl

[2] Mishchenko S., Valenti A., “A Leibniz variety with almost polynomial growth”, Journal of Algebra, 223 (2000), 66–84 | DOI | MR | Zbl

[3] Mishchenko S. P., Fyatkhutdinova Yu. R., “New properties of Lie algebras variety $\mathbf{N_2A}$”, Fundamental'naya i prikladnaya matematika, 17:7 (2012), 165–173

[4] Maltsev A. I., “On algebras with identitical defining relations”, Matematichesky sbornik, 26(68):1 (1950), 19–33 | MR | Zbl

[5] Mishchenko S. P., “Growth of Lie algebras manifolds”, Uspekhi matematicheskikh nauk, 45:6(276) (1990), 25–45

[6] Abanina L. E., Ratseev S. M., “Leibniz algebras manifolds associated with standard identities”, Vestnik Samarskogo gosudarstvennogo universiteta, 2005, no. 6, 36–50

[7] Abanina L. E., Mishchenko S. P., “Some Leibniz algebras manifolds”, Mathematical methods and applications, Works of X mathematical readings of MGSU, 2002, 95–99

[8] Skoraya T. V., “Structure of multilinear part of variety $\widetilde{V}_3$”, Uchenye zapiski OSU, 2012, no. 6(2), 203–212

[9] Skoraya T. V., Shvecova A. V., “New properties of Leibniz algebras manifolds”, Izv. Sarat. Univ. Ser. Matematika. Mekhanika. Informatika, 13:4, Part 2 (2013), 124–129