Zobrazeno 1 - 10
of 55
pro vyhledávání: '"Jedlicka, Premysl"'
We study non-degenerate set-theoretic solutions of the Yang-Baxter equation of multipermutation level 2 which are not 2-reductive. We describe an effective way of constructing such solutions using square-free 2-reductive solutions and two bijections.
Externí odkaz:
http://arxiv.org/abs/2407.00755
Autor:
Jedlicka, Premysl, Pilitowska, Agata
We study the diagonal mappings in non-involutive set-theoretic solutions of the Yang-Baxter equation. We show that, for non-degenerate solutions, they are commuting bijections. This gives the positive answer to the question: ``Is every non-degenerate
Externí odkaz:
http://arxiv.org/abs/2402.15652
Autor:
Jedlička, Přemysl, Pilitowska, Agata
We study 2-reductive non-involutive non-degenerate set-theoretic solutions of the Yang-Baxter equation. We give a combinatorial construction of any such solution of any (even infinite) size. We also prove that solutions associated to a skew left brac
Externí odkaz:
http://arxiv.org/abs/2303.15154
Autor:
Jedlička, Přemysl, Pilitowska, Agata
We give a complete characterization of all indecomposable involutive solutions of the Yang-Baxter equation of multipermutation level~2. In the first step we present a construction of some family of such solutions and in the second step we prove that
Externí odkaz:
http://arxiv.org/abs/2207.02944
Autor:
Bonatto, Marco, Jedlička, Přemysl
Skew braces are algebraic structures related to the solutions of the set-theoretic quantum Yang-Baxter equation. We develop the central nilpotency theory for such algebraic structures in the sense of Freese-McKenzie \cite{comm} and we compare the uni
Externí odkaz:
http://arxiv.org/abs/2109.04389
Publikováno v:
Proc. Amer. Math. Soc. 150 (2022), 4223-4239
We study indecomposable involutive set-theoretic solutions of the Yang-Baxter equation with cyclic permutation groups (cocyclic solutions). In particular, we show that there is no one-to-one correspondence between indecomposable cocyclic solutions an
Externí odkaz:
http://arxiv.org/abs/2107.12319
Autor:
Jedlička, Přemysl, Pilitowska, Agata
Publikováno v:
In Journal of Pure and Applied Algebra April 2024 228(4)
Publikováno v:
Forum Math. 33(5) (2021), 1083-1096
We present a construction of all finite indecomposable involutive solutions of the Yang-Baxter equation of multipermutational level at most 2 with abelian permutation group. As a consequence, we obtain a formula for the number of such solutions with
Externí odkaz:
http://arxiv.org/abs/2011.00229
Autor:
Jedlička, Přemysl, Stanovský, David
We are interested in abstract conditions that characterize homomorphic images of affine quandles. Our main result is a two-fold characterization of this class: one by a property of the displacement group, the other one by a property of the correspond
Externí odkaz:
http://arxiv.org/abs/2006.05946
Publikováno v:
Internat.J.Algebra Comput. 30 (2020), 667-683
We investigate a class of non-involutive solutions of the Yang-Baxter equation which generalize self-distributive (derived) solutions. In particular, we study generalized multipermutation solutions in this class. We show that the Yang-Baxter (permuta
Externí odkaz:
http://arxiv.org/abs/1906.03960