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pro vyhledávání: '"Okniński, J."'
A complete classification of all finite bijective set-theoretic solutions $(S,s)$ to the Pentagon Equation is obtained. First, it is shown that every such a solution determines a semigroup structure on the set $S$ that is the direct product $E\times
Externí odkaz:
http://arxiv.org/abs/2405.20406
To every involutive non-degenerate set-theoretic solution $(X,r)$ of the Yang-Baxter equation on a finite set $X$ there is a naturally associated finite solvable permutation group ${\mathcal G}(X,r)$ acting on $X$. We prove that every primitive permu
Externí odkaz:
http://arxiv.org/abs/2003.01983
Left braces, introduced by Rump, have turned out to provide an important tool in the study of set theoretic solutions of the quantum Yang-Baxter equation. In particular, they have allowed to construct several new families of solutions. A left brace $
Externí odkaz:
http://arxiv.org/abs/2001.08905
Autor:
Cedó, F., Okniński, J.
Publikováno v:
In Advances in Mathematics 1 October 2023 430
Given a finite non-degenerate set-theoretic solution $(X,r)$ of the Yang-Baxter equation and a field $K$, the structure $K$-algebra of $(X,r)$ is $A=A(K,X,r)=K\langle X\mid xy=uv \mbox{ whenever }r(x,y)=(u,v)\rangle$. Note that $A=\oplus_{n\geq 0} A_
Externí odkaz:
http://arxiv.org/abs/1904.11927
Akademický článek
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Autor:
Cedó, F., Okniński, J.
Publikováno v:
In Journal of Algebra 15 June 2022 600:125-151
Autor:
Cedó, F., Okniński, J.
Publikováno v:
In Advances in Mathematics 19 November 2021 391
Iterated matched products of finite braces and simplicity; new solutions of the Yang-Baxter equation
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 $B$, one can construct explicitly all the non-degenerate involutive set-t
Externí odkaz:
http://arxiv.org/abs/1610.00477
Publikováno v:
In Journal of Pure and Applied Algebra January 2021 225(1)