9 citations · 24 across the 12 of their papers we have counts for
14 papers
Set-theoretic solutions of the Yang--Baxter equation, associated quadratic algebras and the minimality condition
F. Cedo, E. Jespers, J. Okninski
Given a finite non-degenerate set-theoretic solution of the Yang-Baxter equation and a field , the structure -algebra of is $A=A(K,X,r)=K\langle X\mid xy=uv \…
Gröbner basis and the automaton property of Hecke--Kiselman algebras
Arkadiusz Mȩcel, Jan Okniński
It is shown that the Hecke-Kiselman algebra associated to a finite directed graph is an automaton algebra in the sense of Ufnarovskii. Consequently, its Gelfand-Kirillov dimension…
Iterated matched products of finite braces and simplicity; new solutions of the Yang-Baxter equation
D. Bachiller, F. Cedó, E. Jespers +1
Braces were introduced by Rump as a promising tool in the study of the set-theoretic solutions of the Yang-Baxter equation. It has been recently proved that, given a left brace …
A family of irretractable square-free solutions of the Yang-Baxter equation
David Bachiller, Ferran Cedo, Eric Jespers +1
A new family of non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation is constructed. All these solutions are strong twisted unions of multipermutation solu…
Braces and the Yang-Baxter equation
Ferran Cedo, Eric Jespers, Jan Okninski
Several aspects of relations between braces and non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation are discussed and many consequences are derived. In pa…
Grobner-Shirshov bases for plactic algebras
Lukasz Kubat, Jan Okninski
A finite Grobner-Shirshov basis is constructed for the plactic algebra of rank 3 over a field K. It is also shown that plactic algebras of rank exceeding 3 do not have finite Grobn…