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Now in paperback, this is a graduate level text for theoretical physicists and mathematicians which systematically lays out the foundations for the subject of Quantum Groups in a clear and accessible way. The topic is developed in a logical manner with quantum groups (Hopf Algebras) treated as mathematical objects in their own right. After formal definitions and basic theory, the book goes on to cover such topics as quantum enveloping algebras, matrix quantum groups, combinatorics, cross products of various kinds, the quantum double, the semiclassical theory of Poisson-Lie groups, the representation theory, braided groups and applications to q-deformed physics. Explicit proofs and many examples will allow the reader quickly to pick up the techniques needed for working in this exciting new field.
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Quantum groups --- Representations of quantum groups --- Groupes quantiques. --- Quantum groups.
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This book focuses on quantum groups, i.e., continuous deformations of Lie groups, and their applications in physics. These algebraic structures have been studied in the last decade by a growing number of mathematicians and physicists, and are found to underlie many physical systems of interest. They do provide, in fact, a sort of common algebraic ground for seemingly very different physical problems. As it has happened for supersymmetry, the q-group symmetries are bound to play a vital role in physics, even in fundamental theories like gauge theory or gravity. In fact q-symmetry can be conside
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Quantum groups. --- Mathematical physics. --- Quantum groups --- Mathematical physics
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An organised step-by-step introduction to the theory of compact quantum groups, starting with examples coming from quantum physics, which stems from the basic undergraduate mathematics curriculum. Introducing more abstract concepts along the way when needed, the reader is led from the fundamentals of the theory to recent research results. The emphasis is put on the combinatorics underlying compact quantum groups, which is very elementary to describe but leads to profound results. This book includes many exercises to help students work through new concepts and ideas and consolidate their understanding. The theory itself is illustrated by an array of examples, some related to other fields of Mathematics such as free probability theory or graph theory. The book is intended for graduate students, motivated undergraduate students and researchers.
Quantum groups. --- Representations of quantum groups. --- Combinatorial analysis.
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The book aims to survey recent developments in quantum algebras and related topics. Quantum groups were introduced by Drinfeld and Jimbo in 1985 in their work on Yang-Baxter equations. The subject from the very beginning has been an interesting one for both mathematics and theoretical physics. For example, Yangian is a special example of quantum group, corresponding to rational solution of Yang-Baxter equation. Viewed as a generalization of the symmetric group, Yangians also have close connections to algebraic combinatorics. This is the proceeding for the International Workshop on Quantized Al
Quantum groups --- Physics --- Quantum theory
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