Hecke algebras for set-theoretical solutions to the Yang--Baxter equation

2024/11/01 by Edouard Feingesicht, Feingesicht, Edouard
Computer Science · Mathematics · #16T25 #20C08 #20N02 #Advanced Algebra and Logic #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2411.00695

openalex publication_date 2024/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define a concept of Hecke algebra for structure groups of set-theoretical solutions to the Yang--Baxter equation. As a comparison to Artin--Tits groups of spherical type, we study some properties of this construction, while also highlighting some differences that appear, which shows a difference between finite Coxeter groups and the "Coxeter-like" group introduced by Dehornoy. We also relate this definition to known constructions on solutions (retractions). Finally, we study a particular case related to Torus Knot groups and Complex Reflexion groups.

Related

• Coxeter-like groups for groups of set-theoretic solutions of the Yang--Baxter equation
• Set-theoretic solutions of the Yang-Baxter equation, RC-calculus, and Garside germs
• On Dehornoy's representation for the Yang-Baxter equation
• Structure groupoids of quiver-theoretic Yang-Baxter maps
• New simple solutions of the Yang--Baxter equation and their permutation groups