Geodesic
$n$-valued quandles and associated bialgebras
Teoretičeskaâ i matematičeskaâ fizika, Tome 220 (2024) no. 1, pp. 25-43 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study $n$-valued quandles and $n$-corack bialgebras. These structures are closely related to topological field theories in dimensions $2$ and $3$, to the set-theoretic Yang–Baxter equation, and to the $n$-valued groups, which have attracted considerable attention or researchers. We elaborate the basic methods of this theory, find an analogue of the so-called coset construction known in the theory of $n$-valued groups, and construct $n$-valued quandles using $n$-multiquandles. In contrast to the case of $n$-valued groups, this construction turns out to be quite rich in algebraic and topological applications. We study the properties of $n$-corack bialgebras, which play a role similar to that of bialgebras in group theory.
Mots-clés : multiset, quandle
Keywords: multivalued group, multigroup, rack, $n$-valued quandle, bialgebra, rack bialgebra. 
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V. G. Bardakov; T. A. Kozlovskaya; D. V. Talalaev. $n$-valued quandles and associated bialgebras. Teoretičeskaâ i matematičeskaâ fizika, Tome 220 (2024) no. 1, pp. 25-43. http://geodesic.mathdoc.fr/item/TMF_2024_220_1_a2/

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