On Quadrirational Yang-Baxter Maps

Abstract

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.

Proceedings of the workshop "Geometric Aspects of Discrete and Ultra-Discrete Integrable Systems" (Glasgow, March-April 2009)

References in corpus (1)

• Yang-Baxter maps: dynamical point of view

Cited by in corpus (31)

• On non-multiaffine consistent-around-the-cube lattice equations
• Integrable Matrix Models in Discrete Space-Time
• Set-theoretical reflection equation: Classification of reflection maps
• On non-abelian quadrirational Yang-Baxter maps
• Tetrahedron maps and symmetries of three dimensional integrable discrete equations
• Families of Integrable Equations
• Invariants in Separated Variables: Yang-Baxter, Entwining and Transfer Maps
• Set theoretic Yang-Baxter equation, braces and Drinfeld twists
• Entwining Yang-Baxter maps related to NLS type equations
• From Braces to Hecke algebras & Quantum Groups
• Yang--Baxter maps, Darboux transformations, and linear approximations of refactorisation problems
• Relativistic Collisions as Yang-Baxter maps
• Idempotent biquadratics, Yang-Baxter maps and birational representations of Coxeter groups
• 3D compatible ternary systems and Yang-Baxter maps
• Non-Abelian hierarchies of compatible maps, associated integrable difference systems and Yang-Baxter maps
• Integrable Boundary for Quad-Graph Systems: Three-Dimensional Boundary Consistency
• Yang-Baxter Maps from the Discrete BKP Equation
• Quandles as pre-Lie skew braces, set-theoretic Hopf algebras & universal R-matrices
• Discrete Lax pairs and hierarchies of integrable difference systems
• An algebraic approach to discrete time integrability
• Multi-quadratic quad equations: integrable cases from a factorised-discriminant hypothesis
• Systems of difference equations on a vector valued function that admit 3D space of scalar potentials
• Darboux transformations, discrete integrable systems and related Yang-Baxter maps
• Discretizations of the generalized AKNS scheme
• Discrete integrable systems, Darboux transformations, and Yang-Baxter maps
• Yang-Baxter maps and independence preserving property
• From Yang-Baxter maps to integrable quad maps and recurrences
• Self-distributive structures, braces & the Yang-Baxter equation
• Classification of integrable boundary equations for integrable quad-graph systems
• On refactorization problems and rational Lax matrices of quadrirational Yang-Baxter maps
• $2^n-$rational maps