Marzia Mazzotta

activity

20192026

most citedRota-Baxter operators on Clifford semigroups and the Yang-Baxter equation

16 citations · 46 across the 14 of their papers we have counts for

collaborators

17 papers

math.QA2026

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 $(S, +, \circ)$ such that both $(S, +)$ and $(S, \circ)$ are inverse semigroups and the following identity ho…

math.GR2026

Right groups, left quasigroups, and right heaps

Andrea Albano, Alberto Facchini, Marzia Mazzotta +1

A right group is a semigroup $(S, \cdot)$ in which, for every $a, b \in S$ , there is a unique $x \in S$ such that $a \cdot x = b$ . In this article, we develop the theory of heaps starting…

math.GR2026

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…

math.QA2025

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…

math.RA2025

Associative Pentagon Algebras

Marzia Mazzotta, Agata Pilitowska

A set-theoretic solution to the Pentagon Equation can be described as a \emph{pentagon} algebra $(S, \cdot, *)$ such that $(S, \cdot)$ is a semigroup and the operations $\cdot$ …

math.RA2024

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…

math.QA2024★ 2 cited

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…

math.QA2023★ 1 cited

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…

math.QA2023★ 3 cited

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…

math.QA2023★ 2 cited

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 $(S, +, \circ)$ including skew braces and giving rise to a set-theoretic solution of the Yang-Baxter equation. We show that…

math.GR2023★ 4 cited

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 $s : S \times S \to S \times S$ on a set $S$ and writing $s (a, b) = (a \cdot b, θ_{a} (b))$ , with $\cdot$ a binary operation on $S$ …

math.QA2023★ 7 cited

Idempotent set-theoretical solutions of the pentagon equation

Marzia Mazzotta

A set-theoretical solution of the pentagon equation on a non-empty set $X$ is a function $s : X \times X \to X \times X$ satisfying the relation $s_{23}\, s_{13}\, s_{12}=s_{12}\, s_{23…

math.QA2022★ 16 cited

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 $(S, +, \circ)$ where $\…

math.QA2021

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…

math.QA2021★ 11 cited

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 $S$ e…

math.QA2019

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 $S$ is a set, a map $s : S \times S \to S \times S$ is said to be a set theoretical soluti…

math.QA2019

Set-theoretical solutions of the pentagon equation on groups

Francesco Catino, Marzia Mazzotta, Maria Maddalena Miccoli

Let $M$ be a set. A set-theoretical solution of the pentagon equation on $M$ is a map $s : M \times M ⟶ M \times M$ such that \begin{equation*} s_{23}\, s_{13}\, s_{12}=s_…