Geodesic
Proper $\mathrm{T}$-ideals of Poisson algebras with extreme properties
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2016), pp. 8-16 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Let $\{\gamma_n(\mathbf{V})\}_{n\ge1}$ be the sequence of proper codimensions of a variety $\mathbf{V}$ of Poisson algebras over a field of characteristic zero. A class of minimal varieties of Poisson algebras of polynomial growth of the sequence $\{\gamma_n(\mathbf{V})\}_{n\ge1}$ is presented, i.e. the sequence $\{\gamma_n(\mathbf{V})\}_{n\ge1}$ of any such variety $\mathbf{V}$ grows as a polynomial of some degree $k$, but the sequence $\{\gamma_n(\mathbf{W})\}_{n\ge1}$ of any proper subvariety $\mathbf{W}$ in $\mathbf{V}$ grows as a polynomial of degree strictly less than $k$. 
@article{VMUMM_2016_6_a1,
     author = {S. M. Ratseev},
     title = {Proper $\mathrm{T}$-ideals of {Poisson} algebras with extreme properties},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {8--16},
     year = {2016},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2016_6_a1/}
}
TY  - JOUR
AU  - S. M. Ratseev
TI  - Proper $\mathrm{T}$-ideals of Poisson algebras with extreme properties
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2016
SP  - 8
EP  - 16
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2016_6_a1/
LA  - ru
ID  - VMUMM_2016_6_a1
ER  - 
%0 Journal Article
%A S. M. Ratseev
%T Proper $\mathrm{T}$-ideals of Poisson algebras with extreme properties
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2016
%P 8-16
%N 6
%U http://geodesic.mathdoc.fr/item/VMUMM_2016_6_a1/
%G ru
%F VMUMM_2016_6_a1
S. M. Ratseev. Proper $\mathrm{T}$-ideals of Poisson algebras with extreme properties. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2016), pp. 8-16. http://geodesic.mathdoc.fr/item/VMUMM_2016_6_a1/

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

[2] Giambruno A., Zaicev M.V., Polynomial identities and asymptotic methods, AMS Math. Surveys and Monogr., 122, Providence R.I., 2005 | DOI | MR | Zbl

[3] Ratseev S.M., “Algebry Puassona polinomialnogo rosta”, Sib. matem. zhurn., 54:3 (2013), 700–711 | MR | Zbl

[4] Mishchenko S.P., Petrogradsky V.M., Regev A., “Poisson PI algebras”, Trans. Amer. Math. Soc., 359:10 (2007), 4669–4694 | DOI | MR | Zbl

[5] Ratseev S.M., “Ekvivalentnye usloviya polinomialnosti rosta mnogoobrazii algebr Puassona”, Vestn. Mosk. un-ta. Matem. Mekhan., 67:5 (2012), 8–13 | MR | Zbl

[6] Volichenko I.B., “Ob odnom mnogoobrazii algebr Li, svyazannom so standartnymi tozhdestvami”, Vestsi AN BSSR: Ser. fiz.-matem. nauk., 1980, no. 1, 23–30 | MR | Zbl

[7] Mattina D.La., “Varieties of almost polynomial growth: classifying their subvarieties”, Manuscripta Math., 123:2 (2007), 185–203 | DOI | MR | Zbl