The retraction relation for biracks

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60460709%3A41310%2F19%3A79156" target="_blank" >RIV/60460709:41310/19:79156 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0022404918302883?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022404918302883?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jpaa.2018.11.020" target="_blank" >10.1016/j.jpaa.2018.11.020</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The retraction relation for biracks

Popis výsledku v původním jazyce

Etingof, Schedler and Soloviev introduced, for each non-degenerate involutive set-theoretical solution (X, sigma, tau) of the Yang-Baxter equation, the equivalence relation similar to defined on the set X and they considered a new non-degenerate involutive induced retraction solution defined on the quotient set X-similar to. It is well known that translating set-theoretical non-degenerate solutions of the Yang-Baxter equation into the universal algebra language we obtain an algebra called a birack. In the paper we introduce the generalized retraction relation approximate to on a birack, which is equal to similar to in an involutive case. We present a complete algebraic proof that the relation approximate to is a congruence of the birack. Thus we show that the retraction of a set-theoretical non-degenerate solution is well defined not only in the involutive case but also in the case of all non-involutive solutions.

Název v anglickém jazyce

The retraction relation for biracks

Popis výsledku anglicky

Etingof, Schedler and Soloviev introduced, for each non-degenerate involutive set-theoretical solution (X, sigma, tau) of the Yang-Baxter equation, the equivalence relation similar to defined on the set X and they considered a new non-degenerate involutive induced retraction solution defined on the quotient set X-similar to. It is well known that translating set-theoretical non-degenerate solutions of the Yang-Baxter equation into the universal algebra language we obtain an algebra called a birack. In the paper we introduce the generalized retraction relation approximate to on a birack, which is equal to similar to in an involutive case. We present a complete algebraic proof that the relation approximate to is a congruence of the birack. Thus we show that the retraction of a set-theoretical non-degenerate solution is well defined not only in the involutive case but also in the case of all non-involutive solutions.

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

2019

Kód důvěrnosti údajů

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

Název periodika

JOURNAL OF PURE AND APPLIED ALGEBRA

ISSN

0022-4049

e-ISSN

0022-4049

Svazek periodika

233

Číslo periodika v rámci svazku

8

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

17

Strana od-do

3594-3610

Kód UT WoS článku

000462422200022

EID výsledku v databázi Scopus

2-s2.0-85056324081