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RESEARCH PRODUCT

The Structure Group and the Permutation Group of a Set-Theoretic Solution of the Quantum Yang–Baxter Equation

N. Fuster-corralH. MengAdolfo Ballester-bolinchesRamon Esteban-romeroRamon Esteban-romero

subject

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

description

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.

yearjournalcountryeditionlanguage
2021-06-04Mediterranean Journal of Mathematics
https://doi.org/10.1007/s00009-021-01793-7