We consider one-dimensional quantum circuits of the brickwork type, where the fundamental
quantum gate is dual unitary. Such models are solvable: the dynamical correlation functions …

Our primary focus is on the theory of skew braces, specifically exploring their connection
with combinatorial solutions to the Yang–Baxter equation. Skew braces have recently …

We consider one dimensional block cellular automata, where the local update rules are
given by Yang-Baxter maps, which are set theoretical solutions of the Yang-Baxter …

This article focuses on indecomposable involutive non-degenerate set-theoretical solutions
to the Yang–Baxter equation. More specifically, we give a full classification of those solutions …

Motivated by the proof of Rump of a conjecture of Gateva–Ivanova on the decomposability of
square-free solutions to the Yang–Baxter equation, we present several other …

We present a construction of all finite indecomposable involutive solutions of the Yang–
Baxter equation of multipermutational level at most 2 with abelian permutation group. As a …

In this paper we study the problem of the classification of indecomposable solutions of the
Yang-Baxter equation. Using a scheme proposed by Bachiller, Cedó, and Jespers, and …

We give a complete characterization of all indecomposable involutive solutions of the Yang-
Baxter equation of multipermutation level 2. In the first step we present a construction of …

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 …

Braces are ring-like structures equivalent to groups G with a G-module structure such that
the identity map is a 1-cocycle. By comparison, crystallographic groups give rise to 1 …