4 papers · 1 filter
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…
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…
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.…