Non-linear Equations, Quantum Groups and Duality Theorems (Paperback)

The importance of the Yang-Baxter equation to a variety of branches in mathematics and physics is well known. Its solutions are intimately related to quantum groups, knot theory, exactly solvable statistical mechanical models, quantum and classical integrable models, etc. In this book, we present a new method to construct solutions for the Yang-Baxter equation. Our method can be applied for solving other equations in Quantum Group Theory. Also, this book provides a categorical interpretation for the construction of the Yang-Baxter operators derived from (co)algebra structures, leading to the extension of the duality between the finite dimensional algebra and coalgebra structures. Other topics included in this book are: Lie (co)algebras, a unification theory in Hopf Algebra Theory, etc. We hope that this book will help other mathematicians and physicists researching on the Yang-Baxter equation and its applications. It can also be used for (parts of) graduate courses on the Yang-Baxter equations, Quantum Groups and Hopf Algebras.