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…