The complete solution to the constant quantum Yang-Baxter equation in two dimensions

Abstract

We describe how the complete solution to the two-dimensional constant quantum Yang-Baxter equation [J. Hietarinta, Phys. Lett. A165,245(1992)] was found. (Talk presented at the XIX International Colloquium on Group Theoretical Methods in Physics.)

4 pages, LaTeX

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• Boundary solutions of the quantum Yang-Baxter equation and solutions in three dimensions
• Non-hermitian integrable systems from constant non-invertible solutions of the Yang-Baxter equation
• Exceptional solutions to the eight-vertex model and integrability of anisotropic extensions of massive fermionic models
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• All Link Invariants for Two Dimensional Solutions of Yang-Baxter Equation and Dressings
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• Quantum integrability of a massive anisotropic SU(N) fermionic model
• Dichotomy theorem separating complete integrability and non-integrability of isotropic spin chains
• Novel approach of exploring ASEP-like models through the Yang Baxter Equation
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• All 4 x 4 solutions of the quantum Yang-Baxter equation
• Almost local integrable models from supersymmetry algebras
• Two-State Spectral-Free Solutions of Frenkel-Moore Simplex Equation
• On the parametrization of solutions of the Yang--Baxter equations
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• Explicit R-matrices for inhomogeneous 3D chiral Potts models: Integrability and the action formulation for
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• On Integrability of Many-Body Problems with Point Interactions