Marzia Mazzotta

activity

20242026

collaborators

9 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.RA2026

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.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.QA2025

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…