Diagonals of solutions of the Yang-Baxter equation

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Diagonals of solutions of the Yang-Baxter equation

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Diagonals of solutions of the Yang-Baxter equation

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

FORUM MATHEMATICUM

ISSN

0933-7741

e-ISSN

0933-7741

Svazek periodika

38

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

18

Strana od-do

321-338

Kód UT WoS článku

001499067300001

EID výsledku v databázi Scopus

2-s2.0-105007356631