Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Communications in Theoretical Physics

Braiding Matrix with a Spectral Parameter for the Quantum Octet Representation

Yu-Dong Yin, Zhong-Qi Ma

Published Oct 1, 1991• 0 citations
Publisher

Abstract

In this paper the spectrum-dependent solution of the Yang-Baxter equation related to the statistical face model (braiding matrix) for the octet representation of the quantum enveloping algebra is computed explicitly. In this example there is multiplicity greater than one in the decomposition of the coproduct .
DOI
10.1088/0253-6102/16/3/303

Related papers

BRAIDING MATRIX WITH A SPECTRAL PARAMETER FOR THE QUANTUM OCTET REPRESENTATION

殷育东, 马中骐, Yadong Yin +1 more

In this paper the spectrum-dependent solution of the Yang-Baxter equation related to the statistical face model (braiding matrix) for the octet representation of the quantum sl(3) enveloping algebra is computed explicitly. In this example there is multiplicity greater than one in the decomposition of the coproduct 8 x 8.

•Jan 1, 1991•0 citations

Solutions of Yang–Baxter equation in the vertex model and the face model for octet representation

Bo-Yu Hou, Bo-Yuan Hou, Zhong-Qi Ma +1 more

In this paper, the solutions of the Yang–Baxter equation both in the vertex model (R matrix) and in the face model (braiding matrix) are computed explicitly for the octet representation of the quantum Kac–Moody A(1)2 enveloping algebra where there is multiplicity greater than one in the decomposition of the coproduct 8⊗8.

Journal of Mathematical Physics•Aug 1, 1991•3 citations

Braiding and Fusion Matrices for Quantum Octet Representation

Zhong-Qi Ma, Yu-Dong Yin

The braiding and fusion matrices based on the octet representation of the quantum sl(3) enveloping algebra are computed. The multiplicity in the decomposition of the coproduct 8 × 8 manifests itself in those matrices.

Communications in Theoretical Physics•Jun 1, 1990•1 citation

Quantum Group Construction of Non-standard R-matrix for Yang-Baxter Equation

Mo‐Lin Ge, Sun Changpu, Kang Xue

By taking the concept of weight conservation into account, new solutions of Yang-Baxter equation without spectral parameter are obtained through the non-standard R-matrix on the tensorial space V 1/2 ⊗ V j ( j ≠ 1/2) in terms of the irreducible representation of the quantum universal enveloping algebra SL q (2). The non-standard R-matrix R 1/2 1 is obtained in an explicit form for j = 1.

Chinese Physics Letters•Oct 1, 1991•0 citations

Yang-Baxter solutions from commuting operators

Pramod Padmanabhan, Kun Hao, V. E. Korepin

We construct $R$-matrices (with a multidimensional spectral parameter) that include additive as well as non-additive parameters. They satisfy the colored Yang-Baxter equation. The solutions depend on a set of commuting operators. They change with the representation of the latter. The associated Yang-Baxter algebra and the spectrum of the transfer matrix are also studied.

arXiv:2401.05662•Jan 11, 2024•0 citations

Yang-Baxter Equation and Quantum Enveloping Algebras

Zhong-Qi Ma

The exact solution of C.N. Yang's one-dimensional many-body problem with repulsive delta-function interactions and R.J. Baxter's eight-vertex statistical model are brilliant achievements in many-body statistical physics. A nonlinear equation, now known as the Yang-Baxter equation, is the key to the solution of both problems. The Yang-Baxter equation has also come to play an important role in such diverse topics as completely integrable statistical models, conformal and topological field theories, knots and links, braid groups and quantum enveloping algebras. This pioneering textbook attempts to make accessible results in this rapidly-growing area of research. The author presents the mathematical fundamentals at the outset, then develops an intuitive understanding of Hopf algebras, quantisation of Lie bialgebras and quantum enveloping algebras. The historical derivation of the Yang-Baxter equation from statistical models is recounted, and the interpretation and solution of the equation are systematically discussed. Throughout, emphasis is placed on acquiring calculation skills through physical understanding rather than achieving mathematical rigour. Originating from the author's own research experience and lectures, this book will prove both an excellent graduate text and a useful work of reference

WORLD SCIENTIFIC eBooks•Dec 1, 1993•61 citations
We construct RRR-matrices (with a multidimensional spectral parameter) that include additive as well as non-additive parameters. They satisfy the colored Yang-Baxter equation. The solutions depend on a set of commuting operators. They change with the representation of the latter. The associated Yang-Baxter algebra and the spectrum of the transfer matrix are also studied.
The exact solution of C.N. Yang's one-dimensional many-body problem with repulsive delta-function interactions and R.J. Baxter's eight-vertex statistical model are brilliant achievements in many-body statistical physics. A nonlinear equation, now known as the Yang-Baxter equation, is the key to the solution of both problems. The Yang-Baxter equation has also come to play an important role in such diverse topics as completely integrable statistical models, conformal and topological field theories, knots and links, braid groups and quantum enveloping algebras. This pioneering textbook attempts to make accessible results in this rapidly-growing area of research. The author presents the mathematical fundamentals at the outset, then develops an intuitive understanding of Hopf algebras, quantisation of Lie bialgebras and quantum enveloping algebras. The historical derivation of the Yang-Baxter equation from statistical models is recounted, and the interpretation and solution of the equation are systematically discussed. Throughout, emphasis is placed on acquiring calculation skills through physical understanding rather than achieving mathematical rigour. Originating from the author's own research experience and lectures, this book will prove both an excellent graduate text and a useful work of reference