16 citations · 77 across the 22 of their papers we have counts for
23 papers
Right groups, left quasigroups, and right heaps
Andrea Albano, Alberto Facchini, Marzia Mazzotta +1
A right group is a semigroup in which, for every , there is a unique such that . In this article, we develop the theory of heaps starting…
Action accessibility in the variety of skew braces
Andrea Albano, Paola Stefanelli
In this paper, we answer negatively to a question posed in the context of the 2025 Oberwolfach Mini-Workshop ``The Yang-Baxter Equation and Representations of Braid Groups'' regard…
Right groups and the set-theoretic Yang-Baxter equation
Andrea Albano, Alberto Facchini, Marzia Mazzotta +1
In this paper, we provide techniques to obtain left non-degenerate set-theoretic solutions of the Yang-Baxter equation, drawing on the class of right groups. To this end, we introd…
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…
Generalized digroups, di-skew braces, and solutions of the set-theoretic Yang-Baxter equation
Andrea Albano, Paola Stefanelli
We introduce a novel algebraic structure called di-skew brace by which we show that generalized digroups systematically yield bijective, non-degenerate solutions to the set-theoret…
Parametric reflection maps: an algebraic approach
Anastasia Doikou, Marzia Mazzotta, Paola Stefanelli
We study solutions of the parametric set-theoretic reflection equation from an algebraic perspective by employing recently derived generalizations of the familiar shelves and racks…
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…
Quandles as pre-Lie skew braces, set-theoretic Hopf algebras & universal R-matrices
Anastasia Doikou, Bernard Rybolowicz, Paola Stefanelli
We present connections between left non-degenerate solutions of the set-theoretic braid equation and left shelves using Drinfel'd homomorphisms. We generalize the notion of affine…
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…
Set-theoretical solutions of the pentagon equation on Clifford semigroups
Marzia Mazzotta, Vicent Pérez-Calabuig, Paola Stefanelli
Given a set-theoretical solution of the pentagon equation on a set and writing , with a binary operation on …
Affine structures on groups and semi-braces
Paola Stefanelli
We introduce affine structures on groups and show they form a category equivalent to that of semi-braces. In particular, such a new description of semi-braces includes that present…
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…
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…
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…