16 citations · 42 across the 11 of their papers we have counts for
14 papers
On set-theoretic solutions of pentagon equation and positive basis Hopf algebras
Ilaria Colazzo, Geoffrey Janssens
We investigate the connection between bijective, not necessarily finite, set-theoretic solutions of the pentagon equation and Hopf algebras. Firstly, we prove that finite solutions…
On the cabling of non-involutive set-theoretic solutions of the Yang--Baxter equation
Ilaria Colazzo, Arne Van Antwerpen
We extend the cabling method by Lebed, Ramírez and Vendramin from involutive to bijective non-degenerate set-theoretic solutions of the Yang--Baxter equation by working in the Yang…
Bijective solutions to the Pentagon Equation
I. Colazzo, J. Okniński, A. Van Antwerpen
A complete classification of all finite bijective set-theoretic solutions to the Pentagon Equation is obtained. First, it is shown that every such solution determines a sem…
Skew bracoids containing a skew brace
Ilaria Colazzo, Alan Koch, Isabel Martin-Lyons +1
Skew bracoids have been shown to have applications in Hopf-Galois theory. We show that a certain family of skew bracoids correspond bijectively with left cancellative semibraces. A…
Simple solutions of the Yang-Baxter equation
Ilaria Colazzo, Eric Jespers, Łukasz Kubat +1
We study simple set-theoretic solutions of the Yang-Baxter equation that are finite and non-degenerate. Such retractable solutions are fully described and to investigate the irretr…
Structure algebras of finite set-theoretic solutions of the Yang--Baxter equation
Ilaria Colazzo, Eric Jespers, Łukasz Kubat +1
Quadratic algebras related to some classes of finite left non-degenerate solutions (X,r) of the Yang--Baxter equation have been intensively studied since they are the associative r…
Finite idempotent set-theoretic solutions of the Yang--Baxter equation
Ilaria Colazzo, Eric Jespers, Łukasz Kubat +2
It is proven that finite idempotent left non-degenerate set-theoretic solutions of the Yang-Baxter equation on a set are determined by a left simple semigroup structure…
On derived-indecomposable solutions of the Yang--Baxter equation
Ilaria Colazzo, Maria Ferrara, Marco Trombetti
If is a finite non-degenerate set-theoretic solution of the Yang--Baxter equation, the additive group of the structure skew brace is an -group, i.e. a group wh…
Left non-degenerate set-theoretic solutions of the Yang-Baxter equation and semitrusses
Ilaria Colazzo, Eric Jespers, Arne Van Antwerpen +1
To determine and analyze arbitrary left non-degenerate set-theoretic solutions of the Yang-Baxter equation (not necessarily bijective), we introduce an associative algebraic struct…
Set-theoretic solutions to the Yang-Baxter equation and generalized semi-braces
Francesco Catino, Ilaria Colazzo, Paola Stefanelli
This paper aims to introduce a construction technique of set-theoretic solutions of the Yang-Baxter equation, called strong semilattice of solutions. This technique, inspired by th…
Set-theoretic solutions of the Pentagon Equation
Ilaria Colazzo, Eric Jespers, Lukasz Kubat
A set-theoretic solution of the Pentagon Equation on a non-empty set is a map such that , where $s_{12}=s\times\mathrm{id}…
The algebraic structure of left semi-trusses
Ilaria Colazzo, Arne Van Antwerpen
The distributive laws of ring theory are fundamental equalities in algebra. However, recently in the study of the Yang-Baxter equation, many algebraic structures with alternative "…
The matched product of set-theoretical solutions associated with shelves
Francesco Catino, Ilaria Colazzo, Paola Stefanelli
We investigate the matched product of solutions associated with right and left shelves. First, we prove that the requirements to provide the matched product of solutions that come…
The matched product of the solutions to the Yang-Baxter equation of finite order
Francesco Catino, Ilaria Colazzo, Paola Stefanelli
In this work, we focus on the set-theoretical solutions of the Yang-Baxter equation which are of finite order and not necessarily bijective. We use the matched product of solutions…