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math.QA2024
Coprime extensions of indecomposable solutions to the Yang-Baxter equation
Carsten Dietzel
In this article, we introduce a method to extend involutive nondegenerate set-theoretic solutions to the Yang--Baxter equation by means of equivariant mappings to graded modules, t…
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.QA2024
Indecomposable involutive set-theoretical solutions to the Yang-Baxter equation of size
Carsten Dietzel, Silvia Properzi, Senne Trappeniers
The quantum Yang-Baxter equation is a braiding condition on vector spaces which is of high relevance in several fields of mathematics, such as knot theory and quantum group theory.…