16 citations · 46 across the 14 of their papers we have counts for
12 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…
Quasi racks, quasi bijective and quasi non-degenerate set-theoretic solutions of the Yang-Baxter equation
Marzia Mazzotta, Paola Stefanelli, Magdalena Wiertel
This work initiates a systematic study of the class of quasi bijective and quasi non-degenerate solutions to the set-theoretic Yang-Baxter equation. The motivation stems from the o…
Reflections to set-theoretic solutions of the Yang-Baxter equation
Andrea Albano, Marzia Mazzotta, Paola Stefanelli
The main aim of this paper is to determine reflections to bijective and non-degenerate solutions of the Yang-Baxter equation, by exploring their connections with their derived solu…
Set-theoretical solutions to the pentagon equation: a survey
Marzia Mazzotta
This survey aims to collect the main results of the theory of the set-theoretical solutions to the pentagon equation obtained up to now in the literature. In particular, we present…
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…
Deformed solutions of the Yang-Baxter equation associated to dual weak braces
Marzia Mazzotta, Bernard Rybołowicz, Paola Stefanelli
A dual weak brace is an algebraic structure including skew braces and giving rise to a set-theoretic solution of the Yang-Baxter equation. We show that…
Idempotent set-theoretical solutions of the pentagon equation
Marzia Mazzotta
A set-theoretical solution of the pentagon equation on a non-empty set is a function satisfying the relation $s_{23}\, s_{13}\, s_{12}=s_{12}\, s_{23…
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 $\…
Simplicity and finite primitive level of indecomposable set-theoretic solutions of the Yang-Baxter equation
Marco Castelli, Marzia Mazzotta, Paola Stefanelli
This paper aims to deepen the theory of bijective non-degenerate set-theoretic solutions of the Yang-Baxter equation, not necessarily involutive, by means of q-cycle sets. We entir…
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…
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…
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_…