Zobrazeno 1 - 10
of 390
pro vyhledávání: '"Jespers, E."'
Publikováno v:
Commun. Contemp. Math. 25 (2023), no. 09, Paper No. 2250064
We study relations between different notions of nilpotency in the context of skew braces and applications to the structure of solutions to the Yang-Baxter equation. In particular, we consider annihilator nilpotent skew braces, an important class that
Externí odkaz:
http://arxiv.org/abs/2205.01572
Given a finite bijective non-degenerate set-theoretic solution $(X,r)$ of the Yang--Baxter equation we characterize when its structure monoid $M(X,r)$ is Malcev nilpotent. Applying this characterization to solutions coming from racks, we rediscover s
Externí odkaz:
http://arxiv.org/abs/2011.01724
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
Publikováno v:
Adv. Math. 385 (2021), 107767
We define the radical and weight of a skew left brace and provide some basic properties of these notions. In particular, we obtain a Wedderburn type decomposition for Artinian skew left braces. Furthermore, we prove analogues of a theorem of Wiegold,
Externí odkaz:
http://arxiv.org/abs/2001.10967
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
Publikováno v:
Math. Ann. 375 (2019), no. 3-4, 1649-1663
We introduce strong left ideals of skew braces and prove that they produce non-trivial decomposition of set-theoretic solutions of the Yang-Baxter equation. We study factorization of skew left braces through strong left ideals and we prove analogs of
Externí odkaz:
http://arxiv.org/abs/1905.05886
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
Publikováno v:
In Journal of Algebra 15 November 2022 610:409-462
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 Advances in Mathematics 16 July 2021 385