Algebraic structures behind the Yang-Baxterization process

被引：0
作者：
Ozdemir, C. [1 ]
Gahramanov, I. [2 ,3 ,4 ,5 ]
机构：
[1] Cayyolu Doga Sci & Technol High Sch, Ankara, Turkiye
[2] Bogazici Univ, Dept Phys, Istanbul, Turkiye
[3] Russian Acad Sci, Steklov Math Inst, Moscow, Russia
[4] Khazar Univ, Dept Math, Baku, Azerbaijan
[5] Azerbaijan Natl Acad Sci, Inst Radiat Problems, Baku, Azerbaijan
来源：
THEORETICAL AND MATHEMATICAL PHYSICS | 2024年 / 221卷 / 02期
基金：
俄罗斯科学基金会;
关键词：
Yang-Baxter equations; braid group; Birman-Murakami-Wenzl algebra; n-CB algebras; exactly solvable models of statistical physics; BAXTER EQUATION; INTEGRABILITY;
D O I：
10.1134/S0040577924110114
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
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.
引用
收藏
页码：1959 / 1980
页数：22
相关论文
共 35 条
  • [1] Akutsu Y., 1989, Braid Group, Knot Theory and Statistical Mechanics, P151, DOI DOI 10.1142/97898127983500007
  • [2] A lemma on systems of knotted curves
    Alexander, JW
    [J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1923, 9 : 93 - 95
  • [3] Artin E., 1926, ABH MATH SEM HAMBURG, V4, P47, DOI DOI 10.1007/BF02950718
  • [4] Baxter R.J, 1982, EXACTLY SOLVED MODEL
  • [5] The 5-CB algebra and fused SU(2) lattice models
    Belavin, Vladimir
    Gepner, Doron
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2021, 54 (37)
  • [6] The 4-CB algebra and solvable lattice models
    Belavin, Vladimir
    Gepner, Doron
    Li, Jian-Rong
    Tessler, Ran
    [J]. JOURNAL OF HIGH ENERGY PHYSICS, 2019, 2019 (11)
  • [7] BRAIDS, LINK POLYNOMIALS AND A NEW ALGEBRA
    BIRMAN, JS
    WENZL, H
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1989, 313 (01) : 249 - 273
  • [8] YANG-BAXTERIZATION OF BRAID GROUP-REPRESENTATIONS
    CHENG, Y
    GE, ML
    XUE, K
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1991, 136 (01) : 195 - 208
  • [9] Drinfeld V.G., 1985, SOV MATH DOKL, V32, P256
  • [10] Gahramanov I., 2022, Integrability from supersymmetric duality: a short review
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