Zobrazeno 1 - 10
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pro vyhledávání: '"Cedó, Ferran"'
Autor:
Cedo, Ferran, Okninski, Jan
For every prime number p and integer $n>1$, a simple, involutive, non-degenerate set-theoretic solution $(X,r$) of the Yang-Baxter equation of cardinality $|X| = p^n$ is constructed. Furthermore, for every non-(square-free) positive integer m which i
Externí odkaz:
http://arxiv.org/abs/2407.07907
Autor:
Cedo, Ferran, Okninski, Jan
A new class of indecomposable, irretractable, involutive, non-degenerate set-theoretic solutions of the Yang--Baxter equation is constructed. This class complements the class of such solutions constructed in \cite{CO22} and together they generalize t
Externí odkaz:
http://arxiv.org/abs/2401.12904
Autor:
Cedó, Ferran, Okniński, Jan
Indecomposable involutive non-degenerate set-theoretic solutions $(X,r)$ of the Yang-Baxter equation of cardinality $p_1\cdots p_n$, for different prime numbers $p_1,\ldots, p_n$, are studied. It is proved that they are multipermutation solutions of
Externí odkaz:
http://arxiv.org/abs/2212.06753
One of the results in our article, which appeared in Publ. Mat. 65 (2021), 499--528, is that the structure monoid $M(X,r)$ of a left non-degenerate solution $(X,r)$ of the Yang-Baxter Equation is a left semi-truss, in the sense of Brzezi\'nski, with
Externí odkaz:
http://arxiv.org/abs/2202.03174
Autor:
Cedó, Ferran, Okniński, Jan
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 solutions is determined and necessary and sufficient conditions are found
Externí odkaz:
http://arxiv.org/abs/2112.07271
Autor:
Cedó, Ferran, Okniński, Jan
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 associated permutation group acts transitively on X. One of the major pr
Externí odkaz:
http://arxiv.org/abs/2012.08400
We introduce left and right series of left semi-braces. This allows to define left and right nilpotent left semi-braces. We study the structure of such semi-braces and generalize some results, known for skew left braces, to left semi-braces. We study
Externí odkaz:
http://arxiv.org/abs/2010.04939
Given a set-theoretic solution $(X,r)$ of the Yang--Baxter equation, we denote by $M=M(X,r)$ the structure monoid and by $A=A(X,r)$, respectively $A'=A'(X,r)$, the left, respectively right, derived structure monoid of $(X,r)$. It is shown that there
Externí odkaz:
http://arxiv.org/abs/1912.09710
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 from a description of all finite left braces has been recently discov
Externí odkaz:
http://arxiv.org/abs/1807.06408
Publikováno v:
Proc. Lond. Math. Soc. (3) 118 (2019), no. 6, 1367-1392
We study series of left ideals of skew left braces that are analogs of upper central series of groups. These concepts allow us to define left and right nilpotent skew left braces. Several results related to these concepts are proved and applications
Externí odkaz:
http://arxiv.org/abs/1806.01127