8 citations · 19 across the 6 of their papers we have counts for
10 papers
New simple solutions of the Yang-Baxter equation and solutions associated to simple left braces
Ferran Cedó, Jan Okniński
Involutive non-degenerate set theoretic solutions of the Yang-Baxter equation are considered, with a focus on finite solutions. A rich class of indecomposable and irretractable sol…
Constructing finite simple solutions of the Yang-Baxter equation
Ferran Cedó, Jan Okniński
We study involutive non-degenerate set-theoretic solutions (X,r) of the Yang-Baxter equation on a finite set X. The emphasis is on the case where (X,r) is indecomposable, so the as…
On the radical of a Hecke-Kiselman algebra
Jan Okniński, Magdalena Wiertel
The Hecke-Kiselman algebra of a finite oriented graph over a field is studied. If is an oriented cycle, it is shown that the algebra is semiprime and its central locali…
Combinatorics and structure of Hecke-Kiselman algebras
Jan Okniński, Magdalena Wiertel
Hecke-Kiselman monoids and their algebras , over a field , associated to finite oriented graphs are studied. In the case is a cycle of…
Plactic monoids satisfy nontrivial identities
Jan Okniński
It is shown that plactic monoids satisfy nontrivial identities.
An abundance of simple left braces with abelian multiplicative Sylow subgroups
Ferran Cedó, Eric Jespers, Jan Okniński
Braces were introduced by Rump to study involutive non-degenerate set-theoretic solutions of the Yang-Baxter equation. A constructive method for producing all such finite solutions…
Algebras with finitely many conjugacy classes of left ideals versus algebras of finite representation type
Arkadiusz Męcel, Jan Okniński
Let A be a finite dimensional algebra over an algebraically closed field with the radical nilpotent of index 2. It is shown that A has finitely many conjugacy classes of left ideal…
Asymmetric product of left braces and simplicity; new solutions of the Yang-Baxter equation
David Bachiller, Ferran Cedó, Eric Jespers +1
The problem of constructing all the non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation recently has been reduced to the problem of describing all the lef…
A note on identities in plactic monoids and monoids of upper-triangular tropical matrices
Alan J. Cain, Georg Klein, Łukasz Kubat +2
This paper uses the combinatorics of Young tableaux to prove the plactic monoid of infinite rank does not satisfy a non-trivial identity, by showing that the plactic monoid of rank…
Irreducible representations of the Chinese monoid
Łukasz Kubat, Jan Okniński
All irreducible representations of the Chinese monoid , of any rank , over a nondenumerable algebraically closed field , are constructed. It turns out that they have a r…