Yang-Baxter Equation and Quantum Enveloping Algebras

This is a textbook examining the Yang-Baxter equation. The Yang-Baxter equation was presented a quarter of a century ago and became one of the main concerns of physicists and mathematicians in recent years. This book arose from lectures given by the author in an attempt to reformulate the results in the rapidly developing research works and make the materials more accessible. It explains the presentation of the Yang-Baxter equation from statistical models, and expounds systematically the meaning and solving methods for this equation. From the viewpoint of theoretical physicists it intends to develop an intuitive understanding of the fundamental knowledge on the Hopf algebras, quantization of Lie bialgebras, and the quantum enveloping algebras, but placing emphasis on the introduction of the calculation skill in terms of the physical language.