Geodesic
Two-dimensional supersymmetric nonlinear equations associated with embeddings of the subsuperalgebra $\mathrm{osp}(1,2)$ in lie superalgebras
Teoretičeskaâ i matematičeskaâ fizika, Tome 61 (1984) no. 1, pp. 150-154 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The paper gives the construction of a large class of two-dimensional supersymmetric nonlinear systems that are associated through a Lax type representation with the local part of an arbitrary Lie superalgebra $\mathfrak G$ with Grassmann structure. The grading of $\mathfrak G$ is realized by the Cartan element of its subsuperalgebra $\mathrm{osp}(l, 2)$. Sufficient conditions are established for exact integrability of the obtained systems, the simplest special ease of which is the supersymmetric generalization of the two-dimensional Toda chain. 
@article{TMF_1984_61_1_a13,
     author = {A. N. Leznov and M. V. Saveliev},
     title = {Two-dimensional supersymmetric nonlinear equations associated with embeddings of the subsuperalgebra $\mathrm{osp}(1,2)$ in lie superalgebras},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {150--154},
     year = {1984},
     volume = {61},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1984_61_1_a13/}
}
TY  - JOUR
AU  - A. N. Leznov
AU  - M. V. Saveliev
TI  - Two-dimensional supersymmetric nonlinear equations associated with embeddings of the subsuperalgebra $\mathrm{osp}(1,2)$ in lie superalgebras
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1984
SP  - 150
EP  - 154
VL  - 61
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1984_61_1_a13/
LA  - ru
ID  - TMF_1984_61_1_a13
ER  - 
%0 Journal Article
%A A. N. Leznov
%A M. V. Saveliev
%T Two-dimensional supersymmetric nonlinear equations associated with embeddings of the subsuperalgebra $\mathrm{osp}(1,2)$ in lie superalgebras
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1984
%P 150-154
%V 61
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1984_61_1_a13/
%G ru
%F TMF_1984_61_1_a13
A. N. Leznov; M. V. Saveliev. Two-dimensional supersymmetric nonlinear equations associated with embeddings of the subsuperalgebra $\mathrm{osp}(1,2)$ in lie superalgebras. Teoretičeskaâ i matematičeskaâ fizika, Tome 61 (1984) no. 1, pp. 150-154. http://geodesic.mathdoc.fr/item/TMF_1984_61_1_a13/

[1] Yu. I. Manin (red.), Geometricheskie idei v fizike, Sb. statei, Mir, M., 1983 ; Van Nieuwenheuzen P., Phys. Rep., 68 (1981), 189 | MR | DOI | MR

[2] Savelev M. V., TMF, 59:3 (1984), 367–372 | MR | Zbl

[3] Leznov A. N., Savelev M. V., Itogi nauki i tekhniki, VINITI AN SSSR. Matem. analiz, 22, VINITI, M., 1984, 101–136 ; Leznov A. N., Saveliev M. V., Commun. Math. Phys., 74 (1980), 111–118 ; 89 (1983), 59–75 | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl

[4] Olshanetsky M. A., Commun. Math. Phys., 88 (1983), 63–76 | DOI | MR | Zbl

[5] Chaichian M., Kulish P. P., Phys. Lett., B78 (1978), 413–416 | DOI | MR

[6] Kostant B., Lecture Notes in Math., 570, 1977, 177–201 ; Kac V. G., Adv. Math., 26 (1977), 8–96 ; Березин Ф. А., Введение в алгебру и анализ с антикоммутирующими переменными, МГУ, М., 1983 | DOI | MR | DOI | Zbl | MR

[7] Leznov A. N., Tochno integriruemye dvumernye dinamicheskie sistemy, svyazannye s supersimmetrichnymi algebrami, Preprint IFVE 83-7, IFVE, Serpukhov, 1983