[PDF] Yang-Baxter equation and quantum enveloping algebras Zhongqi Ma

In the past 30 years, differential geometry has undergone an enormous change with infusion of topology, Lie theory, complex analysis, algebraic geometry and partial differential equations. Professor Matsushima played a leading role in this transformation by bringing new techniques of Lie groups and Lie algebras into the study of real and complex manifolds. This volume is a collection of all the 46 papers written by him This is the first-ever textbook on the Yang-Baxter equation. A key nonlinear equation for solving two important models in many-body statistical theory – the many-body problem in one dimension with repulsive delta-function interaction presented by Professor Baxter in 1972 – it has become one of the main concerns of physicists and mathematicians in the last ten years.A textbook on this subject which also serves as a reference book is vital for an equation which plays important roles in diverse areas of physics and mathematics like the completely integrable statistical models, conformal field theories, topological field theories, the theory of braid groups, the theory of knots and links, etc.This book arose from lectures given by the author in an attempt to reformulate the results of the rapidly developing research and make the material more accessible. It explains the presentation of the Yang-Baxter equation from statistical models, and expound systematically the meaning and methods of solving for this equation.From the viewpoint of theoretical physics it aims to develop an intuitive understanding of the fundamental knowledge of the Hopf algebras, quantization of Lie bialgebras, and the quantum enveloping algebras, and places emphasis on the introduction of the calculation skill in terms of the physical language. ?Read more… Ch. 1. Mathematical Preliminaries — Ch. 2. Historical Origin of the Yang-Baxter Equation — Ch. 3. Classical Yang-Baxter Equation — Ch. 4. Quantum Enveloping Algebras — Ch. 5. Quantum Clebsch-Gordan Coefficients — Ch. 6. Simple Yang-Baxter Equation — Ch. 7. Trigonometric and Rational Solutions — Ch. 8. Non-Generic q Values