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math.RA2023
Simple solutions of the Yang-Baxter equation
Ilaria Colazzo, Eric Jespers, Łukasz 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…
math.RA2018
The structure monoid and algebra of a non-degenerate set-theoretic solution of the Yang-Baxter equation
Eric Jespers, Łukasz Kubat, Arne Van Antwerpen
For a finite involutive non-degenerate solution of the Yang--Baxter equation it is known that the structure monoid is a monoid of I-type, and the structure algebra…
math.RA2010★ 3 cited
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…