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Non-linear Equations, Quantum Groups and Duality Theorems
Angleščina
108 b
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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.
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