Showing math.GRShow all
3 papers · 1 filter
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.GR2024
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.GR2023
Dehornoy's class and Sylows for set-theoretical solutions of the Yang-Baxter equation
Edouard Feingesicht
We explain how the germ of the structure group of a cycle set decomposes as a product of its Sylow-subgroups, and how this process can be reversed to construct cycle sets from ones…