4 papers · 1 filter
On set-theoretic solutions of pentagon equation and positive basis Hopf algebras
Ilaria Colazzo, Geoffrey Janssens
We investigate the connection between bijective, not necessarily finite, set-theoretic solutions of the pentagon equation and Hopf algebras. Firstly, we prove that finite solutions…
Structure algebras of finite set-theoretic solutions of the Yang--Baxter equation
Ilaria Colazzo, Eric Jespers, Åukasz Kubat +1
Quadratic algebras related to some classes of finite left non-degenerate solutions (X,r) of the Yang--Baxter equation have been intensively studied since they are the associative r…
Simple solutions of the Yang-Baxter equation
Ilaria Colazzo, Eric Jespers, Åukasz Kubat +1
We study simple set-theoretic solutions of the Yang-Baxter equation that are finite and non-degenerate. Such retractable solutions are fully described and to investigate the irretr…
Skew bracoids containing a skew brace
Ilaria Colazzo, Alan Koch, Isabel Martin-Lyons +1
Skew bracoids have been shown to have applications in Hopf-Galois theory. We show that a certain family of skew bracoids correspond bijectively with left cancellative semibraces. A…