0000000000460616

AUTHOR

N. Fuster-corral

showing 2 related works from this author

On finite involutive Yang–Baxter groups

2021

[EN] A group G is said to be an involutive Yang¿Baxter group, or simply an IYB-group, if it is isomorphic to the permutation group of an involutive, nondegenerate set-theoretic solution of the Yang-Baxter equation. We give new sufficient conditions for a group that can be factorised as a product of two IYB-groups to be an IYB-group. Some earlier results are direct consequences of our main theorem.

Yang–Baxter equationApplied MathematicsGeneral MathematicsYang-Baxter equationInvolutive nondegenerate solutionsInvolutive Yang-Baxter groupMATEMATICA APLICADAMatemàticaFinite left braceMathematical physicsMathematicsProceedings of the American Mathematical Society
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The Structure Group and the Permutation Group of a Set-Theoretic Solution of the Quantum Yang–Baxter Equation

2021

We describe the left brace structure of the structure group and the permutation group associated to an involutive, non-degenerate set-theoretic solution of the quantum YangBaxter equation by using the Cayley graph of its permutation group with respect to its natural generating system. We use our descriptions of the additions in both braces to obtain new properties of the structure and the permutation groups and to recover some known properties of these groups in a more transparent way.

CombinatoricsSet (abstract data type)Cayley graphYang–Baxter equationGroup (mathematics)Mathematics::Quantum AlgebraGeneral MathematicsStructure (category theory)Permutation groupMatemàticaQuantumMathematicsMediterranean Journal of Mathematics
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