Algebraic structures behind the Yang–Baxterization process

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

Theoretical and Mathematical Physics Pub Date : 2024-11-26 DOI:10.1134/S0040577924110114

C. Özdemir, I. Gahramanov

引用次数: 0

Abstract

We discuss the process of Yang–Baxterization in representations of the braid group. We discuss the role played by \(n\)-CB algebras in Yang–Baxterization. We present diagrams depicting the defining relations for the \(4\)-CB algebras. These relations are illustrated using the isomorphism between the general free algebra generated by \(\{1\}\), \(\{E_i\}\), and \(\{G_i\}\) (the generators of the Birman–Murakami–Wenzl algebra) and Kauffman’s tangle algebra.

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杨-巴克斯特化过程背后的代数结构

我们讨论了辫状群表征中的杨-巴克斯特化过程。我们讨论了 \(n\)-CB 对象在杨-巴克斯特化中扮演的角色。我们用图表描述了 \(4\)-CB 结构的定义关系。我们使用由 \(\{1\}\)、\(\{E_i\}\)和\(\{G_i\}\)（比尔曼-村上-温茨尔代数的生成子）产生的一般自由代数和考夫曼的纠缠代数之间的同构关系来说明这些关系。

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.