Yang-Baxter maps: dynamical point of view

2006/12/28 by А. П. Веселов, Veselov, A. P. · 5 citations
Mathematics · Physics and Astronomy · #37K10 #81R12 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.math/0612814

openalex publication_date 2006/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A review of some recent results on the dynamical theory of the Yang-Baxter 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 several concrete examples.

Citations

• Quantum R-matrices and factorization problems

Cited by

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• On a new integrable discretization of the derivative nonlinear Schrödinger (Chen-Lee-Liu) equation
• Garside structure on monoids with quadratic square-free relations
• Quantum spaces associated to multipermutation solutions of level two
• Multipermutation solutions of the Yang--Baxter equation

Related

• Yang-Baxter maps and matrix solitons
• Lectures on the dynamical Yang-Baxter equations
• Poisson Lie groups and Hamiltonian theory of the Yang-Baxter maps
• Baxterization for the dynamical Yang-Baxter equation
• On the integrability of the transfer dynamics of non-involutive Yang-Baxter maps