Skew Braces and the Braid Equation on Sets

Bernard Rybołowicz

doi:10.1007/978-3-031-62407-0_11

Skew Braces and the Braid Equation on Sets

Bernard Rybołowicz^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

We discuss how skew braces allow us to construct solutions of the braid equation on the underlying set of a skew brace. First, we discuss methods introduced by W. Rump and then generalised by L. Guarnieri and L. Vendramin. Further, we present a recently introduced way of deforming solutions acquired from skew braces. We analyse skew braces of size 4. We linearise the deformed solutions and observe that the Jordan matrix of deformation is different to the original. That leads to the conclusion that deformations give us a tool to manipulate the solution not only up to the change of the basis.

Original language	English
Title of host publication	Geometric Methods in Physics XL. WGMP 2022
Publisher	Birkhäuser
Pages	145-152
Number of pages	8
ISBN (Electronic)	9783031624070
ISBN (Print)	9783031624063, 9783031624094
DOIs	https://doi.org/10.1007/978-3-031-62407-0_11
Publication status	Published - 27 May 2024
Event	XL Workshop on Geometric Methods in Physics 2023 - Białowieża, Poland Duration: 26 Jun 2023 → 30 Jun 2023 https://wgmp.uwb.edu.pl/plakaty/40.jpg

Publication series

Name	Trends in Mathematics
Volume	Part F3359
ISSN (Print)	2297-0215
ISSN (Electronic)	2297-024X

Conference

Conference	XL Workshop on Geometric Methods in Physics 2023
Abbreviated title	WGMP 2023
Country/Territory	Poland
City	Białowieża
Period	26/06/23 → 30/06/23
Internet address	https://wgmp.uwb.edu.pl/plakaty/40.jpg

Keywords

Braid equation
Skew brace
Yang-Baxter equation

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/978-3-031-62407-0_11

Cite this

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title = "Skew Braces and the Braid Equation on Sets",

abstract = "We discuss how skew braces allow us to construct solutions of the braid equation on the underlying set of a skew brace. First, we discuss methods introduced by W. Rump and then generalised by L. Guarnieri and L. Vendramin. Further, we present a recently introduced way of deforming solutions acquired from skew braces. We analyse skew braces of size 4. We linearise the deformed solutions and observe that the Jordan matrix of deformation is different to the original. That leads to the conclusion that deformations give us a tool to manipulate the solution not only up to the change of the basis.",

keywords = "Braid equation, Skew brace, Yang-Baxter equation",

author = "Bernard Rybo{\l}owicz",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.; XL Workshop on Geometric Methods in Physics 2023<br/>, WGMP 2023 ; Conference date: 26-06-2023 Through 30-06-2023",

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Y1 - 2024/5/27

N2 - We discuss how skew braces allow us to construct solutions of the braid equation on the underlying set of a skew brace. First, we discuss methods introduced by W. Rump and then generalised by L. Guarnieri and L. Vendramin. Further, we present a recently introduced way of deforming solutions acquired from skew braces. We analyse skew braces of size 4. We linearise the deformed solutions and observe that the Jordan matrix of deformation is different to the original. That leads to the conclusion that deformations give us a tool to manipulate the solution not only up to the change of the basis.

AB - We discuss how skew braces allow us to construct solutions of the braid equation on the underlying set of a skew brace. First, we discuss methods introduced by W. Rump and then generalised by L. Guarnieri and L. Vendramin. Further, we present a recently introduced way of deforming solutions acquired from skew braces. We analyse skew braces of size 4. We linearise the deformed solutions and observe that the Jordan matrix of deformation is different to the original. That leads to the conclusion that deformations give us a tool to manipulate the solution not only up to the change of the basis.

KW - Braid equation

KW - Skew brace

KW - Yang-Baxter equation

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SN - 9783031624094

T3 - Trends in Mathematics

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BT - Geometric Methods in Physics XL. WGMP 2022

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ER -

Skew Braces and the Braid Equation on Sets

Abstract

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Conference

Keywords

ASJC Scopus subject areas

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