The structure group and the permutation group of a set-theoretic solution of the quantum Yang-Baxter equation

DOI10.1007/s00009-021-01793-7zbMath1475.16036OpenAlexW3172390062MaRDI QIDQ2046650

N. Fuster-Corral, Adolfo Ballester-Bolinches, Ramón Esteban-Romero, Hangyang Meng

Publication date: 26 August 2021

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00009-021-01793-7

zbMATH Keywords

Cayley graphYang-Baxter equationstructure groupleft brace

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Yang-Baxter equations (16T25)

Cites Work

• On the Yang-Baxter equation and left nilpotent left braces
• Group extensions and graphs.
• Braces, radical rings, and the quatum Yang-Baxter equation.
• Semigroups of \(I\)-type
• A decomposition theorem for square-free unitary solutions of the quantum Yang-Baxter equation
• Set-theoretical solutions to the quantum Yang-Baxter equation
• Finite quotients of groups of I-type.
• Braces and the Yang-Baxter equation
• Solutions of the Yang-Baxter equation associated with a left brace.
• Involutive Yang-Baxter groups
• Left Braces: Solutions of the Yang-Baxter Equation
• A combinatorial approach to the set-theoretic solutions of the Yang–Baxter equation
• Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction

This page was built for publication: The structure group and the permutation group of a set-theoretic solution of the quantum Yang-Baxter equation