Diagonals of solutions of the Yang-Baxter equation

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60460709%3A41310%2F25%3A101797" target="_blank" >RIV/60460709:41310/25:101797 - isvavai.cz</a>
Result on the web
<a href="https://www.degruyterbrill.com/document/doi/10.1515/forum-2024-0409/html" target="_blank" >https://www.degruyterbrill.com/document/doi/10.1515/forum-2024-0409/html</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/forum-2024-0409" target="_blank" >10.1515/forum-2024-0409</a>

Result language
angličtina
Original language name
Diagonals of solutions of the Yang-Baxter equation
Original language description
We study the diagonal mappings in non-involutive set-theoretic solutions of the Yang-Baxter equation. We show that, for non-degenerate solutions, they are commuting bijections. This gives the positive answer to the question: "Is every non-degenerate solution bijective?" of Ced & oacute;, Jespers and Verwimp. Additionally, we show that, for a subclass of solutions called k-permutational, only one-sided non-degeneracy suffices to prove that one of the diagonal mappings is invertible. We also present an equational characterization of multipermutation solutions and extend results of Rump, Gateva-Ivanova and Castelli, Mazzotta, Stefanelli about decomposability to non-involutive infinite case. In particular, we show that each, not necessarily involutive, square-free multipermutation solution of finite level and arbitrary cardinality, is always decomposable.
Czech name
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Czech description
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Type
J<sub>imp</sub> - 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

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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