Primitive set-theoretic solutions of the Yang-Baxter equation

2020/03/04 by F. Cedo, Cedo, F., Eric Jespers +3
Computer Science · Mathematics · #20B15 #20F16 #Advanced Graph Theory Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Equations Stability Results #Group Theory (math.GR) #Primary 16T25 #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2003.01983

openalex publication_date 2020/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

To every involutive non-degenerate set-theoretic solution (X,r) of the Yang-Baxter equation on a finite set X there is a naturally associated finite solvable permutation group \mathcal G(X,r) acting on X. We prove that every primitive permutation group of this type is of prime order p. Moreover, (X,r) is then a so called permutation solution determined by a cycle of length p. This solves a problem recently asked by A. Ballester-Bolinches. The result opens a new perspective on a possible approach to the classification problem of all involutive non-degenerate set-theoretic solutions.

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