Reflection equation as a tool for studying solutions to the Yang-Baxter equation

DOI10.1016/j.jalgebra.2021.02.002zbMath1504.16059arXiv2008.01752OpenAlexW3047247823MaRDI QIDQ2153346

Publication date: 4 July 2022

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.01752

zbMATH Keywords

Yang-Baxter equation braid group reflection equation structure monoid structure shelf

Mathematics Subject Classification ID

Braid groups; Artin groups (20F36) Sets with a single binary operation (groupoids) (20N02) Yang-Baxter equations (16T25)

Cites Work

Homology of left non-degenerate set-theoretic solutions to the Yang-Baxter equation
Classification of indecomposable involutive set-theoretic solutions to the Yang-Baxter equation
On the set-theoretical Yang-Baxter equation
Set-theoretic solutions of the Yang-Baxter equation and new classes of $\mathrm{R}$-matrices
Set-theoretic solutions of the Yang-Baxter equation, braces and symmetric groups
Set-theoretic Yang-Baxter \& reflection equations and quantum group symmetries
Combinatorial solutions to the reflection equation
The matched product of set-theoretical solutions of the Yang-Baxter equation
Set-theoretic solutions of the Yang-Baxter equation, RC-calculus, and Garside germs.
On the algebraical braid group
Skew braces and the Yang–Baxter equation
Extended reflection equation algebras, the braid group on a handlebody, and associated link polynomials
Left Braces and the Quantum Yang–Baxter Equation
Set-theoretical reflection equation: classification of reflection maps
On Structure Groups of Set-Theoretic Solutions to the Yang–Baxter Equation
Corrigendum and addendum to “The structure monoid and algebra of a non-degenerate set-theoretic solution of the Yang–Baxter equation”
Set-theoretical solutions to the reflection equation associated to the quantum affine algebra of type $\boldsymbol{A^{(1)}_{n-1}}$
Yang–Baxter and reflection maps from vector solitons with a boundary
Actions of skew braces and set-theoretic solutions of the reflection equation
The structure monoid and algebra of a non-degenerate set-theoretic solution of the Yang–Baxter equation
Non-unitary set-theoretical solutions to the quantum Yang-Baxter equation.
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