Abstract:
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 G with Grassmann
structure. The grading of G is realized by the Cartan
element of its subsuperalgebra 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.
Citation:
A. N. Leznov, M. V. Saveliev, “Two-dimensional supersymmetric nonlinear equations associated with embeddings of the subsuperalgebra osp(1,2) in lie superalgebras”, TMF, 61:1 (1984), 150–154; Theoret. and Math. Phys., 61:1 (1984), 1056–1059
\Bibitem{LezSav84}
\by A.~N.~Leznov, M.~V.~Saveliev
\paper Two-dimensional supersymmetric nonlinear equations associated with embeddings of the subsuperalgebra $\mathrm{osp}(1,2)$ in lie superalgebras
\jour TMF
\yr 1984
\vol 61
\issue 1
\pages 150--154
\mathnet{http://mi.mathnet.ru/tmf5669}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=774215}
\zmath{https://zbmath.org/?q=an:0593.58045}
\transl
\jour Theoret. and Math. Phys.
\yr 1984
\vol 61
\issue 1
\pages 1056--1059
\crossref{https://doi.org/10.1007/BF01038555}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1984AGK6100014}
Linking options:
https://www.mathnet.ru/eng/tmf5669
https://www.mathnet.ru/eng/tmf/v61/i1/p150
This publication is cited in the following 10 articles:
M. Legaré, “Lie Superalgebra Valued Self-Dual Yang-Mills Fields and Symmetry Reduction”, JNMP, 4:3-4 (1997), 383
Jean-Loup Gervais, Lochlainn O'Raifeartaigh, Alexander V. Razumov, Mikhail V. Saveliev, “Gauge conditions for the constrained-WZNW-Toda reductions”, Physics Letters B, 301:1 (1993), 41
F. Delduc, E. Ragoucy, P. Sorba, “Super-Toda theories and W-algebras from superspace Wess-Zumino-Witten models”, Commun.Math. Phys., 146:2 (1992), 403
François Delduc, Jean-Loup Gervais, Mikhail V. Saveliev, “Supersymmetric black holes from Toda theories”, Physics Letters B, 292:3-4 (1992), 295
T Inami, H Kanno, “N=2 super W algebras and generalized N=2 super KdV heirarchies based on Lie superalgebras”, J. Phys. A: Math. Gen., 25:13 (1992), 3729
Takeo Inami, Hiroaki Kanno, “Lie superalgebraic approach to super Toda lattice and generalized super KdV equations”, Commun.Math. Phys., 136:3 (1991), 519
F. Toppan, “On the superLiouville theory”, Physics Letters B, 260:3-4 (1991), 346
Shinobu Hikami, “Anderson localization in a superstring model representation”, Physica A: Statistical Mechanics and its Applications, 167:1 (1990), 149
A. N. Leznov, M. V. Saveliev, Symmetries of Partial Differential Equations, 1989, 213
V. A. Andreev, “Odd bases of Lie superalgebras and integrable equations”, Theoret. and Math. Phys., 72:1 (1987), 758–764
Citation in format AMSBIB
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