منابع مشابه
Lax Matrices for Yang-Baxter Maps
It is shown that for a certain class of Yang-Baxter maps (or set-theoretical solutions to the quantum Yang-Baxter equation) the Lax representation can be derived straight from the map itself. A similar phenomenon for 3D consistent equations on quadgraphs has been recently discovered by A. Bobenko and one of the authors, and by F. Nijhoff.
متن کامل. Q A ] 9 A pr 2 00 3 LAX MATRICES FOR YANG - BAXTER MAPS
It is shown that for a certain class of Yang-Baxter maps (or set-theoretical solutions to the quantum Yang-Baxter equation) the Lax representation can be derived straight from the map itself. A similar phenomenon for 3D consistent equations on quadgraphs has been recently discovered by A. Bobenko and one of the authors, and by F. Nijhoff. Introduction. In 1990 V.G. Drinfeld suggested the proble...
متن کاملOn Quadrirational Yang–Baxter Maps
We use the classification of the quadrirational maps given by Adler, Bobenko and Suris to describe when such maps satisfy the Yang–Baxter relation. We show that the corresponding maps can be characterized by certain singularity invariance condition. This leads to some new families of Yang–Baxter maps corresponding to the geometric symmetries of pencils of quadrics.
متن کاملYang-Baxter maps and integrable dynamics
The hierarchy of commuting maps related to a set-theoretical solution of the quantum Yang-Baxter equation (Yang-Baxter map) is introduced. They can be considered as dynamical analogues of the monodromy and/or transfer-matrices. The general scheme of producing Yang-Baxter maps based on matrix factorisation is discussed in the context of the integrability problem for the corresponding dynamical s...
متن کاملYang-Baxter maps: dynamical point of view
A review of some recent results on the dynamical theory of the YangBaxter maps (also known as set-theoretical solutions to the quantum Yang-Baxter equation) is given. The central question is the integrability of the transfer dynamics. The relations with matrix factorisations, matrix KdV solitons, Poisson Lie groups, geometric crystals and tropical combinatorics are discussed and demonstrated on...
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ژورنال
عنوان ژورنال: Journal of Nonlinear Mathematical Physics
سال: 2003
ISSN: 1776-0852
DOI: 10.2991/jnmp.2003.10.s2.8