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Электронный каталог: Isaev, A. P. - Quantum Groups and Yang-Baxter Equations
Isaev, A. P. - Quantum Groups and Yang-Baxter Equations
Статья
Автор: Isaev, A. P.
Natural Science Review: Quantum Groups and Yang-Baxter Equations
б.г.
ISBN отсутствует
Автор: Isaev, A. P.
Natural Science Review: Quantum Groups and Yang-Baxter Equations
б.г.
ISBN отсутствует
На полку
Статья
Isaev, A.P.
Quantum Groups and Yang-Baxter Equations / A.P.Isaev. – Text: electronic // Natural Science Review. – 2025. – No. 2. – P. 100204. – URL: https://nsr-jinr.ru/index.php/nsr/article/view/42/34. – Bibliogr.: 326.
This introductory review is devoted to the newest section of the theory of symmetries — the theoryof quantum groups. The principles of the theory of quantum groups are reviewed from the point ofview of the possibility of their use for deformations of symmetries in physics models. The R-matrix approach to the theory of quantum groups is discussed in detail and is taken as the basis of the quantization of classical Lie groups, as well as some Lie supergroups. We start by laying out the foundations of noncommutative and noncocommutative Hopf algebras. Much attention has been paid to the Hecke and Birman–Murakami–Wenzl (BMW)R-matrices and related quantum matrix algebras .Noncommutative differential geometry on quantum groups of special types is discussed. Trigonometric solutions of the Yang–Baxter equations associated with the quantum groups GL&sub(q)(N),SOq(N),Sp&sub(q)(2n)and supergroups GL&sub(q)(N|M),Osp&sub(q)(N|2m), as well as their rational (Yangian) limits, are presented. Rational R-matrices for exceptional Lie algebras and elliptic solutions of the Yang–Baxter equation are also considered. The basic concepts of the group algebra of the braid group and its finite-dimensional quotients (such as the Hecke and BMW algebras) are outlined. A sketch of the representation theories of the Hecke and BMW algebras is given, including methods for finding idempotents (quantum Young projectors) and their quantum dimensions. Applications of the theory of quantum groups and Yang–Baxter equations in various areas of theoretical physics are briefly discussed.This is a modified version of the review paper published in 2004 as a preprint [47] of the Max-Planck-Institut f ̈ur Mathematik (MPIM) in Bonn.
ОИЯИ = ОИЯИ (JINR)2025
Спец.(статьи,препринты) = С 323 б - Квантовые алгебры. Суперсимметричная квантовая механика. Парастатистики . Анионы. Прочие схемы квантования
Isaev, A.P.
Quantum Groups and Yang-Baxter Equations / A.P.Isaev. – Text: electronic // Natural Science Review. – 2025. – No. 2. – P. 100204. – URL: https://nsr-jinr.ru/index.php/nsr/article/view/42/34. – Bibliogr.: 326.
This introductory review is devoted to the newest section of the theory of symmetries — the theoryof quantum groups. The principles of the theory of quantum groups are reviewed from the point ofview of the possibility of their use for deformations of symmetries in physics models. The R-matrix approach to the theory of quantum groups is discussed in detail and is taken as the basis of the quantization of classical Lie groups, as well as some Lie supergroups. We start by laying out the foundations of noncommutative and noncocommutative Hopf algebras. Much attention has been paid to the Hecke and Birman–Murakami–Wenzl (BMW)R-matrices and related quantum matrix algebras .Noncommutative differential geometry on quantum groups of special types is discussed. Trigonometric solutions of the Yang–Baxter equations associated with the quantum groups GL&sub(q)(N),SOq(N),Sp&sub(q)(2n)and supergroups GL&sub(q)(N|M),Osp&sub(q)(N|2m), as well as their rational (Yangian) limits, are presented. Rational R-matrices for exceptional Lie algebras and elliptic solutions of the Yang–Baxter equation are also considered. The basic concepts of the group algebra of the braid group and its finite-dimensional quotients (such as the Hecke and BMW algebras) are outlined. A sketch of the representation theories of the Hecke and BMW algebras is given, including methods for finding idempotents (quantum Young projectors) and their quantum dimensions. Applications of the theory of quantum groups and Yang–Baxter equations in various areas of theoretical physics are briefly discussed.This is a modified version of the review paper published in 2004 as a preprint [47] of the Max-Planck-Institut f ̈ur Mathematik (MPIM) in Bonn.
ОИЯИ = ОИЯИ (JINR)2025
Спец.(статьи,препринты) = С 323 б - Квантовые алгебры. Суперсимметричная квантовая механика. Парастатистики . Анионы. Прочие схемы квантования
