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

Kód výsledku v 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>
Výsledek na webu
<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>

Jazyk výsledku
angličtina
Název v původním jazyce
Skew left braces and 2-reductive solutions of the Yang-Baxter equation
Popis výsledku v původním jazyce
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.
Název v anglickém jazyce
Skew left braces and 2-reductive solutions of the Yang-Baxter equation
Popis výsledku anglicky
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.

Rok uplatnění
2024
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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