5 papers
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…
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…