n-valued quandles and associated bialgebras Full article
| Journal |
Theoretical and Mathematical Physics (Russian Federation)
ISSN: 0040-5779 , E-ISSN: 1573-9333 |
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| Output data | Year: 2024, Volume: 220, Number: 1, Pages: 1080-1096 Pages count : 17 DOI: 10.1134/s0040577924070031 | ||||||||||
| Tags | multiset, multivalued group, multigroup, rack, quandle, n-valued quandle, bialgebra, rack bialgebra | ||||||||||
| Authors |
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| Affiliations |
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Funding (3)
| 1 | Russian Science Foundation | 20-71-10110 |
| 2 | Министерство науки и высшего образования РФ | 075-02-2023-943 |
| 3 | Фонд развития теоретической физики и математики «БАЗИС» | 23-7-2-14-1 |
Abstract:
We study n-valued quandles and n-corack bialgebras. These structures are closely related to topological f ield 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, f ind 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.
Cite:
Bardakov V.G.
, Kozlovskaya T.A.
, Talalaev D.V.
n-valued quandles and associated bialgebras
Theoretical and Mathematical Physics (Russian Federation). 2024. V.220. N1. P.1080-1096. DOI: 10.1134/s0040577924070031 WOS Scopus РИНЦ OpenAlex
n-valued quandles and associated bialgebras
Theoretical and Mathematical Physics (Russian Federation). 2024. V.220. N1. P.1080-1096. DOI: 10.1134/s0040577924070031 WOS Scopus РИНЦ OpenAlex
Original:
Бардаков В.Г.
, Козловская Т.А.
, Талалаев Д.В.
n-значные квандлы и ассоциированные биалгебры
Теоретическая и математическая физика. 2024. Т.220. №1. С.25-43. DOI: 10.4213/tmf10656 РИНЦ OpenAlex
n-значные квандлы и ассоциированные биалгебры
Теоретическая и математическая физика. 2024. Т.220. №1. С.25-43. DOI: 10.4213/tmf10656 РИНЦ OpenAlex
Dates:
| Submitted: | Dec 12, 2023 |
| Accepted: | Feb 26, 2024 |
| Published print: | Jul 27, 2024 |
| Published online: | Sep 27, 2024 |
Identifiers:
| Web of science: | WOS:001281188400004 |
| Scopus: | 2-s2.0-85199889331 |
| Elibrary: | 68545044 |
| OpenAlex: | W4401053521 |
Citing:
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