3 papers
math.GR2026
On Dehornoy's representation for the Yang-Baxter equation
Carsten Dietzel, Edouard Feingesicht, Silvia Properzi
This article investigates Dehornoy's monomial representations for structure groups and Coxeter-like groups associated with a set-theoretic solution to the Yang--Baxter equation. Us…
math.GR2025
How structure groups and monoids grow
Carsten Dietzel, Edouard Feingesicht, Victoria Lebed
The structure groups and monoids of set-theoretic solutions to the Yang-Baxter Equation can be regarded as deformations of free abelian groups resp. monoids. In this work, we obtai…
math.QA2024
Hecke algebras for set-theoretical solutions to the Yang--Baxter equation
Edouard Feingesicht
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 stu…