16 citations · 62 across the 13 of their papers we have counts for
14 papers · 1 filter
Set-theoretic solutions of the Yang-Baxter equation from inverse braces
Francesco Catino, Marzia Mazzotta, Susanna Tieni
We introduce the algebraic structure of an inverse brace, namely, a triple such that both and are inverse semigroups and the following identity ho…
Solutions of the Yang-Baxter equation and strong semilattices of skew braces
Francesco Catino, Marzia Mazzotta, Paola Stefanelli
We prove that any set-theoretic solution of the Yang-Baxter equation associated to a dual weak brace is a strong semilattice of non-degenerate bijective solutions. This fact makes…
Rota-Baxter operators on Clifford semigroups and the Yang-Baxter equation
Francesco Catino, Marzia Mazzotta, Paola Stefanelli
In this paper, we introduce the theory of Rota-Baxter operators on Clifford semigroups, useful tools for obtaining dual weak braces, i.e., triples where $\…
Set-theoretic solutions of the Yang-Baxter equation associated to weak braces
Francesco Catino, Marzia Mazzotta, Maria Maddalena Miccoli +1
We investigate a new algebraic structure which always gives rise to a set-theoretic solution of the Yang-Baxter equation. Specifically, a weak (left) brace is a non-empty set e…
Indecomposable involutive set-theoretic solutions of the Yang-Baxter equation and orthogonal dynamical extensions of cycle sets
Marco Castelli, Francesco Catino, Paola Stefanelli
Employing the algebraic structure of the left brace and the dynamical extensions of cycle sets, we investigate a class of indecomposable involutive set-theoretic solutions of the Y…
Nilpotency in left semi-braces
Francesco Catino, Ferran Cedó, Paola Stefanelli
We introduce left and right series of left semi-braces. This allows to define left and right nilpotent left semi-braces. We study the structure of such semi-braces and generalize s…
Inverse semi-braces and the Yang-Baxter equation
Francesco Catino, Marzia Mazzotta, Paola Stefanelli
The main aim of this paper is to provide set-theoretical solutions of the Yang-Baxter equation that are not necessarily bijective, among these new idempotent ones. In the specific,…
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…
Left non-degenerate set-theoretic solutions of the Yang-Baxter equation and dynamical extensions of q-cycle sets
Marco Castelli, Francesco Catino, Paola Stefanelli
A first aim of this paper is to give sufficient conditions on left non-degenerate bijective set-theoretic solutions of the Yang-Baxter equation so that they are non-degenerate. In…
Set-theoretical solutions of the Yang-Baxter and pentagon equations on semigroups
Francesco Catino, Marzia Mazzotta, Paola Stefanelli
The Yang-Baxter and pentagon equations are two well-known equations of Mathematical Physic. If is a set, a map is said to be a set theoretical soluti…
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…
About a question of Gateva-Ivanova and Cameron on square-free set-theoretic solutions of the Yang-Baxter equation
Marco Castelli, Francesco Catino, Giuseppina Pinto
In this paper, we introduce a new sequence to find a new estimation of the cardinality of the minimal involutive square-free solution of level . As an applicat…
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…
Set-theoretical solutions of the pentagon equation on groups
Francesco Catino, Marzia Mazzotta, Maria Maddalena Miccoli
Let be a set. A set-theoretical solution of the pentagon equation on is a map such that \begin{equation*} s_{23}\, s_{13}\, s_{12}=s_…