Skew Left Braces of Nilpotent Type

Ferran Cedo; Agata Smoktunowicz; Leonardo Vendramin

doi:10.1112/plms.12209

Skew Left Braces of Nilpotent Type

Ferran Cedo, Agata Smoktunowicz, Leonardo Vendramin

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study series of left ideals of skew left braces that are analogs of upper central series of groups. These concepts allow us to dene left and right nilpotent skew left braces. Several results related to these concepts are proved and applications to innite left braces are given. Indecomposable solutions of the Yang-Baxter equation are explored using the structure of skew left braces.

Original language	English
Pages (from-to)	1367-1392
Journal	Proceedings of the London Mathematical Society
Volume	118
Issue number	6
Early online date	10 Oct 2018
DOIs	https://doi.org/10.1112/plms.12209
Publication status	Published - Jun 2019

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10.1112/plms.12209

R1CedoSmokVendramin (002)Accepted author manuscript, 375 KBLicence: Creative Commons: Attribution-NonCommercial-ShareAlike (CC BY-NC-SA)

Enhancing Representation Theory, Noncommutative Algebra And Geometry Through Moduli, Stability And Deformations
Gordon, I. (Principal Investigator), Bayer, A. (Co-investigator) & Smoktunowicz, A. (Co-investigator)
EPSRC
1/05/18 → 30/04/24
Project: Research
Combinatorial methods in noncommutative ring theory (COIMBRA)
Smoktunowicz, A. (Principal Investigator)
EU government bodies
1/06/13 → 31/05/18
Project: Research

Agata Smoktunowicz
- School of Mathematics - Personal Chair in Algebra
Person: Academic: Research Active

Cite this

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title = "Skew Left Braces of Nilpotent Type",

abstract = "We study series of left ideals of skew left braces that are analogs of upper central series of groups. These concepts allow us to dene left and right nilpotent skew left braces. Several results related to these concepts are proved and applications to innite left braces are given. Indecomposable solutions of the Yang-Baxter equation are explored using the structure of skew left braces.",

author = "Ferran Cedo and Agata Smoktunowicz and Leonardo Vendramin",

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AU - Cedo, Ferran

AU - Smoktunowicz, Agata

AU - Vendramin, Leonardo

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N2 - We study series of left ideals of skew left braces that are analogs of upper central series of groups. These concepts allow us to dene left and right nilpotent skew left braces. Several results related to these concepts are proved and applications to innite left braces are given. Indecomposable solutions of the Yang-Baxter equation are explored using the structure of skew left braces.

AB - We study series of left ideals of skew left braces that are analogs of upper central series of groups. These concepts allow us to dene left and right nilpotent skew left braces. Several results related to these concepts are proved and applications to innite left braces are given. Indecomposable solutions of the Yang-Baxter equation are explored using the structure of skew left braces.

U2 - 10.1112/plms.12209

DO - 10.1112/plms.12209

M3 - Article

SN - 0024-6115

VL - 118

SP - 1367

EP - 1392

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

IS - 6

ER -

Skew Left Braces of Nilpotent Type

Abstract

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Projects

Enhancing Representation Theory, Noncommutative Algebra And Geometry Through Moduli, Stability And Deformations

Combinatorial methods in noncommutative ring theory (COIMBRA)

Profiles

Agata Smoktunowicz

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