Skew left braces and 2-reductive solutions of the Yang-Baxter equation

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60460709%3A41310%2F24%3A97833" target="_blank" >RIV/60460709:41310/24:97833 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1016/j.jpaa.2023.107514" target="_blank" >https://doi.org/10.1016/j.jpaa.2023.107514</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jpaa.2023.107514" target="_blank" >10.1016/j.jpaa.2023.107514</a>

Result language

angličtina

Original language name

Skew left braces and 2-reductive solutions of the Yang-Baxter equation

Original language description

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 brace are 2-reductive if and only if the skew left brace is nilpotent of class 2. Moreover, all such skew left braces are actually bi-skew left braces. We focus on these structures and we give several equivalent properties characterizing solutions associated to bi-skew left braces.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

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Continuities

S - Specificky vyzkum na vysokych skolach

Publication year

2024

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

JOURNAL OF PURE AND APPLIED ALGEBRA

ISSN

0022-4049

e-ISSN

0022-4049

Volume of the periodical

228

Issue of the periodical within the volume

2024-04-01

Country of publishing house

CZ - CZECH REPUBLIC

Number of pages

25

Pages from-to

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UT code for WoS article

001122795400001

EID of the result in the Scopus database

2-s2.0-85169066219