A~criterion for polynomial growth of varieties of Lie superalgebras
Izvestiya. Mathematics , Tome 62 (1998) no. 5, pp. 953-967.

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

A description is obtained of the varieties of Lie superalgebras over a field of characteristic zero whose growth function is asymptotically bounded by a polynomial of some degree.
@article{IM2_1998_62_5_a3,
     author = {M. V. Zaicev and S. P. Mishchenko},
     title = {A~criterion for polynomial growth of varieties of {Lie} superalgebras},
     journal = {Izvestiya. Mathematics },
     pages = {953--967},
     publisher = {mathdoc},
     volume = {62},
     number = {5},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1998_62_5_a3/}
}
TY  - JOUR
AU  - M. V. Zaicev
AU  - S. P. Mishchenko
TI  - A~criterion for polynomial growth of varieties of Lie superalgebras
JO  - Izvestiya. Mathematics 
PY  - 1998
SP  - 953
EP  - 967
VL  - 62
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1998_62_5_a3/
LA  - en
ID  - IM2_1998_62_5_a3
ER  - 
%0 Journal Article
%A M. V. Zaicev
%A S. P. Mishchenko
%T A~criterion for polynomial growth of varieties of Lie superalgebras
%J Izvestiya. Mathematics 
%D 1998
%P 953-967
%V 62
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1998_62_5_a3/
%G en
%F IM2_1998_62_5_a3
M. V. Zaicev; S. P. Mishchenko. A~criterion for polynomial growth of varieties of Lie superalgebras. Izvestiya. Mathematics , Tome 62 (1998) no. 5, pp. 953-967. http://geodesic.mathdoc.fr/item/IM2_1998_62_5_a3/

[1] Regev A., “Existence of identities in $A\otimes B$”, Israel J. Math., 11 (1972), 131–152 | DOI | MR | Zbl

[2] Volichenko I. B., “O mnogoobrazii algebr Li $AN_2$ nad polem kharakteristiki nul”, DAN BSSR, 26:12 (1981), 1063–1066 | MR

[3] Petrogradskii V. M., “O tipakh sverkheksponentsialnogo rosta tozhdestv v PI-algebrakh Li”, Fundamentalnaya i prikl. matematika, 1:4 (1995), 989–1007 | MR | Zbl

[4] Drensky V., Regev A., “Exact asymptotic behaviour of the codimensions of some P.I. algebras”, Israel J. Math., 96 (1996), 231–242 | DOI | MR | Zbl

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

[6] Kemer A. R., “Shpekhtovost $T$-idealov s polinomialnym rostom korazmernostei”, Sib. matem. zhurn., 19 (1978), 54–69 | MR | Zbl

[7] Benediktovich I. I., Zalesskii A. E., “$T$-idealy svobodnoi algebry Li s polinomialnym rostom posledovatelnosti korazmernostei”, Vesti AN BSSR, 1981, no. 3, 5–10 | MR

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

[9] Mischenko S. P., “Rost mnogoobrazii algebr Li”, UMN, 45:6 (1990), 25–45 | Zbl

[10] Scheunert M., The Theory of Lie Superalgebras. An Introduction, Lect. Notes Math., 716, Springer-Verlag, 1979 | MR | Zbl

[11] Bahturin Yu. A., Mikhalev A. A., Petrogradsky V. M., Zaicev M. V., Infinite-dimensional Lie superalgebras, Walter de Gruyter, Berlin, 1992 | MR

[12] Zaitsev M. V., “Lokalno predstavimye mnogoobraziya superalgebr Li”, Matem. zametki, 52:5 (1992), 33–41 | MR

[13] Dzheims G., Teoriya predstavlenii simmetricheskikh grupp, Mir, M., 1982 | MR

[14] Bakhturin Yu. A., Drenski V. S., “Tozhdestva razreshimykh tsvetnykh superalgebr Li”, Algebra i logika, 26:4 (1987), 403–418 | MR