The retraction relation for biracks

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
The retraction relation for biracks
Original language description
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.
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
—
OECD FORD branch
10101 - Pure mathematics

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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