Skew left braces of nilpotent type

被引：54

作者：

Cedo, Ferran ^{[1
]}

Smoktunowicz, Agata ^{[2
]}

Vendramin, Leandro ^{[3
,4
]}

机构：

[1] Univ Autonoma Barcelona, Dept Matemat, Bellaterra Barcelon 08193, Spain

[2] Univ Edinburgh, Sch Math, James Clerk Maxwell Bldg,Kings Bldg,Mayfield Rd, Edinburgh EH9 3JZ, Midlothian, Scotland

[3] Consejo Nacl Invest Cient & Tecn, IMAS, Pabellon 1,Ciudad Univ,C1428EGA, Buenos Aires, DF, Argentina

[4] Univ Buenos Aires, Dept Matemat, FCEN, Pabellon 1,Ciudad Univ,C1428EGA, Buenos Aires, DF, Argentina

来源：

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY | 2019年 / 118卷 / 06期

基金：

英国工程与自然科学研究理事会;

关键词：

16T25 (primary); 81R50 (secondary); SET-THEORETIC SOLUTIONS; YANG-BAXTER EQUATION; HOPF-GALOIS STRUCTURES; MULTIPERMUTATION SOLUTIONS; CLASSIFICATION; EXTENSIONS; CONJECTURE; RINGS;

D O I：

10.1112/plms.12209

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 to infinite left braces are given. Indecomposable solutions of the Yang-Baxter equation are explored using the structure of skew left braces.

引用

页码：1367 / 1392

页数：26

共 50 条

[31] NILPOTENT GROUPS OF CLASS THREE AND BRACES
Cedo, Ferran
Jespers, Eric
Okninski, Jan
PUBLICACIONS MATEMATIQUES, 2016, 60 (01) : 55 - 79
[32] Generalized skew derivations with nilpotent values on left ideals of rings and Banach algebras
Liu, Cheng-Kai
Chen, Hung-Yuan
Liau, Pao-Kuei
LINEAR & MULTILINEAR ALGEBRA, 2014, 62 (04): : 453 - 465
[33] Solutions of the Yang-Baxter equation associated to skew left braces, with applications to racks
Bachiller, David
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2018, 27 (08)
[34] Rota-Baxter groups, skew left braces, and the Yang-Baxter equation
Bardakov, Valeriy G.
Gubarev, Vsevolod
JOURNAL OF ALGEBRA, 2022, 596 : 328 - 351
[35] Skew left braces and isomorphism problems for Hopf-Galois structures on Galois extensions
Koch, Alan
Truman, Paul J.
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2023, 22 (05)
[36] Skew left braces and 2-reductive solutions of the Yang-Baxter equation
Jedlicka, Premysl
Pilitowska, Agata
JOURNAL OF PURE AND APPLIED ALGEBRA, 2024, 228 (04)
[37] Skew Braces of Size p2q I: Abelian Type
Acri, E.
Bonatto, M.
ALGEBRA COLLOQUIUM, 2022, 29 (02) : 297 - 320
[38] Skew Braces and the Braid Equation on Sets
Rybolowicz, Bernard
GEOMETRIC METHODS IN PHYSICS XL, WGMP 2022, 2024, : 145 - 152
[39] Symmetric skew braces and brace systems
Bardakov, Valeriy G.
Neshchadim, Mikhail V.
Yadav, Manoj K.
FORUM MATHEMATICUM, 2023, 35 (03) : 713 - 738
[40] Semidirect products of digroups and skew braces
Facchini, Alberto
Pompili, Mara
BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 2024, 31 (01) : 40 - 53

← 1 2 3 4 5 →