valued quandles and associated bialgebras

valued quandles and associated bialgebras

We study -valued quandles and -corack bialgebras. These structures are closely related to topological field theories in dimensions and , to the set-theoretic Yang–Baxter equation, and to the -valued groups, which have attracted considerable attention or researchers. We elaborate the basic methods of...

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Veröffentlicht in:Theoretical and mathematical physics 2024, Vol.220 (1), p.1080-1096
Hauptverfasser: Bardakov, V. G., Kozlovskaya, T. A., Talalaev, D. V.
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container_title Theoretical and mathematical physics
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creator Bardakov, V. G.
Kozlovskaya, T. A.
Talalaev, D. V.
description We study -valued quandles and -corack bialgebras. These structures are closely related to topological field theories in dimensions and , to the set-theoretic Yang–Baxter equation, and to the -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 -valued groups, and construct -valued quandles using -multiquandles. In contrast to the case of -valued groups, this construction turns out to be quite rich in algebraic and topological applications. We study the properties of -corack bialgebras, which play a role similar to that of bialgebras in group theory.
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639/766/189
639/766/530
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Applications of Mathematics
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Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
Topology
title valued quandles and associated bialgebras
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