$$n$$ -valued quandles and associated bialgebras

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Theoretical and Mathematical Physics Pub Date : 2024-07-27 DOI:10.1134/s0040577924070031

V. G. Bardakov, T. A. Kozlovskaya, D. V. Talalaev

引用次数: 0

Abstract

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.

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$$n$$ 有值准绳和相关双贝叶斯

Abstract We study $n$-valued quandles and $n$-corack bialgebras.这些结构与维数为 $2$ 和 $3$ 的拓扑场论、集合论杨-巴克斯特方程以及 $n$-valued 群密切相关，已经引起了研究者们的极大关注。我们详细阐述了这一理论的基本方法，找到了在$n$值群理论中已知的所谓coset构造的类似物，并用$n$-multiquandles构造了$n$-valued quandles。与（n）值群的情况不同，这种构造在代数学和拓扑学上的应用相当丰富。我们研究了 $n$-corack 双桥的性质，它的作用类似于群论中的双桥。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Theoretical and Mathematical Physics 物理-物理：数学物理

CiteScore

1.60

自引率

20.00%

发文量

103

审稿时长

4-8 weeks

期刊介绍： Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems. Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.