Non-linear Equations, Quantum Groups and Duality Theorems

ISBN-13: 9783639171563 / Angielski / Miękka / 2009 / 72 str.

Florin Nichita

Opis

The importance of the Yang-Baxter equation to avariety of branches in mathematics and physics iswell known. Its solutions are intimately related toquantum groups, knot theory, exactly solvablestatistical mechanical models, quantum and classicalintegrable models, etc.In this book, we present a new method to constructsolutions for the Yang-Baxter equation. Our methodcan be applied for solving other equations in QuantumGroup Theory. Also, this book provides a categoricalinterpretation for the construction of theYang-Baxter operators derived from (co)algebrastructures, leading to the extension of the dualitybetween the finite dimensional algebra and coalgebrastructures. Other topics included in this book are:Lie (co)algebras, a unification theory in HopfAlgebra Theory, etc. We hope that this book will help other mathematiciansand physicists researching on the Yang-Baxterequation and its applications. It can also be usedfor (parts of) graduate courses on the Yang-Baxterequations, Quantum Groups and Hopf Algebras.

O autorze

Dr. Florin Felix Nichita is a Scientific Researcher II (Associate
Professor) at the Institute of Mathematics "Simion Stoilow" of
the Romanian Academy. He received his Ph.D. degree from the State
University of New York at Buffalo (USA). He was awarded a Marie
Curie Fellowship by the European Commission at the University of
Wales Swansea (UK).