1 citations · 1 across the 18 of their papers we have counts for
18 papers
On indecomposable involutive solutions to the Yang-Baxter equation whose squaring map is a -cycle
Marco Castelli, Arpan Kanrar
The pioneering work of Rump, which proved Gateva-Ivanova's conjecture concerning the decomposability of square-free solutions to the Yang-Baxter equation, significantly motivated f…
One-generator skew braces and indecomposable set-theoretic solutions to the Yang-Baxter equation
Marco Castelli
We study the class of one-generator solutions to the Yang-Baxter equation, extending some recent results concerning the classes of involutive and multipermutation solutions. Moreov…
Involutive (simple) latin solutions of the Yang-Baxter equation and related (left) quasigroups
Marco Bonatto, Marco Castelli
In this paper, we study involutive non-degenerate set-theoretic solutions of the Yang-Baxter equation with regular displacement group. In particular, we completely describe the blo…
A note on semiprime skew left braces and related semidirect products
Marco Castelli
In this paper, we focus on semiprime skew left braces provided by semidirect products. We show that if a semidirect product is semiprime and is Artinian, the…
On commutative set-theoretic solutions of the Pentagon Equation
Marco Castelli
We extend the so-called retract relation given in [6] for involutive set-theoretic solutions of the Pentagon Equation and we introduce the notion of associated permutation group to…
On the indecomposable involutive solutions of the Yang-Baxter equation of finite primitive level
Marco Castelli
In this paper, we study the class of indecomposable involutive solutions of the Yang-Baxter equation of finite primitive level, recently introduced by Cedó and Okniński in \cite{ce…
On uniconnected solutions of the Yang-Baxter equation and Dehornoy's class
Marco Castelli, Santiago Ramírez
In the first part, we focus on indecomposable involutive solutions of the Yang-Baxter equation whose permutation group forces them to be uniconnected. Indecomposable involutive sol…
Studying solutions of the Yang-Baxter equation through skew braces, with an application to indecomposable involutive solutions with abelian permutation group
Marco Castelli, Senne Trappeniers
We connect properties of set-theoretic solutions to the Yang--Baxter equation to properties of their permutation skew brace. In particular, a variation of the multipermutation leve…
Left seminear-rings, groups semidirect products and left cancellative left semi-braces
Marco Castelli
We study some relations between left cancellative left semi-braces and other existing algebraic structures. In particular, we show that every left semi-brace arises from a left sem…
A characterization of finite simple set-theoretic solutions of the Yang-Baxter equation
Marco Castelli
In this paper we present a characterization of finite simple involutive non-degenerate set-theoretic solutions of the Yang-Baxter equation by means of left braces and we provide so…
Classification of uniconnected involutive solutions of the Yang-Baxter equation with odd size and a Z-group permutation group
Marco Castelli
In the first part of this paper, we investigate the retraction of finite uniconnected involutive non-degenerate set-theoretic solutions of the Yang-Baxter equation by means of left…
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…
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…
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…
On the indecomposable involutive set-theoretic solutions of the Yang-Baxter equation of prime-power size
Marco Castelli, Giuseppina Pinto, Wolfgang Rump
We develop a method to construct all the indecomposable involutive set-theoretic solutions of the Yang-Baxter equation with a prime-power number of elements and cyclic permutation…
Modified Zakharov-Kuznetsov equation on rectangles
Marcos Castelli, Gleb Doronin
Initial-boundary value problem for the modified Zakharov-Kuznetsov equation posed on a bounded rectangle is considered. The main difficulty is the critical power in nonlinear term.…
Subcritical and critical generalized Zakharov-Kuznetsov equation posed on bounded rectangles
Marcos Castelli, Gleb Doronin
Initial-boundary value problem for the generalized Zakharov-Kuznetsov equation posed on a bounded rectangle is considered. Critical and subcritical powers in nonlinearity are studi…
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…