New Solutions to the Reflection Equation with Braces

2019/05/29 by Kyriakos Katsamaktsis, Katsamaktsis, Kyriakos
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1905.12711

openalex publication_date 2019/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The reflection equation of Cherednik is a counterpart to the celebrated Yang-Baxter equation, with importance in the theory of integrable systems. We obtain several new solutions of the reflection equation using braces building on the work of Smoktunowicz, Vendramin and Weston. In particular, we show that every brace yields several simple solutions and that a natural class of solutions is a near-ring. We find more solutions for factorizable rings. Some of our solutions apply to the original parameter-dependent equation.

Citations

• Eight-vertex model in lattice statistics and one-dimensional anisotropic heisenberg chain. I. Some fundamental eigenvectors
• Boundary conditions for integrable quantum systems

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