9 papers
Proof of Rump's Retraction Conjecture for Quasilinear Cycle Sets
Carsten Dietzel
Nondegenerate cycle sets were introduced by Rump as an algebraic framework for nondegenerate, involutive solutions to the Yang--Baxter equation. Nondegenerate cycle set structures…
Non-degeneracy of Killing forms on real conjugacy classes of finite groups
Carsten Dietzel, Charlotte Roelants
Killing forms on finite groups arise as special cases of braided Killing forms on braided Lie algebras. If is a conjugation-stable subset of a finite group , the K…
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…
Groups of -type
Carsten Dietzel
In this work, we address a question posed by Dehornoy et al. in the book "Foundations of Garside Theory" that asks for a theory of groups of -type when is a Garsi…
Endocabling of involutive solutions to the Yang-Baxter equation, with an application to solutions whose diagonal is a cyclic permutation
Carsten Dietzel
In this article, we introduce endocabling as a technique to deform involutive, non-degenerate set-theoretic solutions to the Yang-Baxter equation (``solutions'', for short) by mean…
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…
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…
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.…
On the enumeration of finite -algebras
C. Dietzel, P. Menchón, L. Vendramin
We use Constraint Satisfaction Methods to construct and enumerate finite -algebras up to isomorphism. These objects were recently introduced by Rump and appear in Garside theory…