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What is a classical r-matrix?
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This article is published in Functional Analysis and Its Applications.The article was published on 1984-01-01. It has received 793 citations till now.read more
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Quantum $R$ matrix for the generalized Toda system
TL;DR: In this paper, the explicit form of the quantumR matrix in the fundamental representation for the generalized Toda system associated with non-exceptional affine Lie algebras is given.
Journal ArticleDOI
Dressing transformations and Poisson group actions
TL;DR: In this paper, les proprietes de Poisson explique les transformations d'habillage en theorie des solitons, and explique le transformation of a homonym.
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Multiparameter quantum groups and twisted quasitriangular Hopf algebras
TL;DR: On montre comment on peut obtenir des groupes quantiques multiparametres a partir des algebres de Hopf torsadees.
Journal Article
Poisson-Nijenhuis structures
TL;DR: In this article, the deformation and dualization of the derivations of the algebra of forms and of the Schouten bracket of multivectors were studied, and the Nijenhuis operator was defined by a Poisson bivector.
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Central extensions of quantum current groups
TL;DR: In this paper, Hopf algebras which are central extensions of quantum current groups are described, and new types of generators for quantum current algebra and its central extension for quantum simple Lie groups are obtained.
References
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Integration of nonlinear equations of mathematical physics by the method of inverse scattering. II
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On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-devries type equations
TL;DR: In this article, the Lie geometric structure behind the Hamiltonian structure of the Korteweg deVries type equations was studied and the authors showed that it is the same as the Lie geometry behind the Lie structure of a Hamiltonian lattice.