Quantum Groups Hopf Algebras And Applications

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Quantum Groups Hopf Algebras And Applications

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Author : Susan Montgomery
language : en
Publisher: American Mathematical Society
Release Date : 2025-03-13

Quantum Groups Hopf Algebras And Applications written by Susan Montgomery and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-13 with Mathematics categories.

This volume contains the proceedings of the AMS Special Session on Quantum Groups, Hopf Algebras, and Applications (in memory of Professor Earl J. Taft), which was held from October 22?23, 2022, at the University of Utah, Salt Lake City, Utah. Hopf algebras play a crucial role in many areas of mathematics, from finite groups to tensor categories, and allows researchers to make many connections between these subjects. Applications of Hopf algebras to low dimensional topology, topological quantum field theory, and condensed matter physics provide further motivation for the study of representations of Hopf algebras and their generalizations. In memory of Earl Jay Taft, a pioneer of the theory of Hopf algebras, this volume collects research articles on Hopf algebras, quantum groups, and tensor categories contributed by prominent researchers. The articles in this volume manifest the diversity and richness of the subject and contain exciting new results which will certainly have applications to different areas of mathematics and physics.

Quantum Groups And Their Representations

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Author : Anatoli Klimyk
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Quantum Groups And Their Representations written by Anatoli Klimyk and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

This book start with an introduction to quantum groups for the beginner and continues as a textbook for graduate students in physics and in mathematics. It can also be used as a reference by more advanced readers. The authors cover a large but well-chosen variety of subjects from the theory of quantum groups (quantized universal enveloping algebras, quantized algebras of functions) and q-deformed algebras (q-oscillator algebras), their representations and corepresentations, and noncommutative differential calculus. The book is written with potential applications in physics and mathematics in mind. The basic quantum groups and quantum algebras and their representations are given in detail and accompanied by explicit formulas. A number of topics and results from the more advanced general theory are developed and discussed.

Introduction To Quantum Groups

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Author : George Lusztig
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-27

Introduction To Quantum Groups written by George Lusztig and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-27 with Mathematics categories.

The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo in 1985, or variations thereof. The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of the theory are provided with canonical basis with rather remarkable properties. This book will be of interest to mathematicians working in the representation theory of Lie groups and Lie algebras, knot theorists and to theoretical physicists and graduate students. Since large parts of the book are independent of the theory of perverse sheaves, the book could also be used as a text book.

Lectures On Algebraic Quantum Groups

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Author : John C Brown
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-04-01

Lectures On Algebraic Quantum Groups written by John C Brown and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-04-01 with Mathematics categories.

This book consists of an expanded set of lectures on algebraic aspects of quantum groups. It particularly concentrates on quantized coordinate rings of algebraic groups and spaces and on quantized enveloping algebras of semisimple Lie algebras. Large parts of the material are developed in full textbook style, featuring many examples and numerous exercises; other portions are discussed with sketches of proofs, while still other material is quoted without proof.

Foundations Of Quantum Group Theory

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Author : Shahn Majid
language : en
Publisher: Cambridge University Press
Release Date : 2000

Foundations Of Quantum Group Theory written by Shahn Majid and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Group theory categories.

A graduate level text which systematically lays out the foundations of Quantum Groups.

Hopf Algebras And Their Actions On Rings

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Author : Susan Montgomery
language : en
Publisher: American Mathematical Soc.
Release Date : 1993-10-28

Hopf Algebras And Their Actions On Rings written by Susan Montgomery and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-10-28 with Mathematics categories.

The last ten years have seen a number of significant advances in Hopf algebras. The best known is the introduction of quantum groups, which are Hopf algebras that arose in mathematical physics and now have connections to many areas of mathematics. In addition, several conjectures of Kaplansky have been solved, the most striking of which is a kind of Lagrange's theorem for Hopf algebras. Work on actions of Hopf algebras has unified earlier results on group actions, actions of Lie algebras, and graded algebras. This book brings together many of these recent developments from the viewpoint of the algebraic structure of Hopf algebras and their actions and coactions. Quantum groups are treated as an important example, rather than as an end in themselves. The two introductory chapters review definitions and basic facts; otherwise, most of the material has not previously appeared in book form. Providing an accessible introduction to Hopf algebras, this book would make an excellent graduate textbook for a course in Hopf algebras or an introduction to quantum groups.

A Guide To Quantum Groups

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Author : Vyjayanthi Chari
language : en
Publisher: Cambridge University Press
Release Date : 1995-07-27

A Guide To Quantum Groups written by Vyjayanthi Chari and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-07-27 with Mathematics categories.

Since they first arose in the 1970s and early 1980s, quantum groups have proved to be of great interest to mathematicians and theoretical physicists. The theory of quantum groups is now well established as a fascinating chapter of representation theory, and has thrown new light on many different topics, notably low-dimensional topology and conformal field theory. The goal of this book is to give a comprehensive view of quantum groups and their applications. The authors build on a self-contained account of the foundations of the subject and go on to treat the more advanced aspects concisely and with detailed references to the literature. Thus this book can serve both as an introduction for the newcomer, and as a guide for the more experienced reader. All who have an interest in the subject will welcome this unique treatment of quantum groups.

Affine Lie Algebras And Quantum Groups

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Author : Jürgen Fuchs
language : en
Publisher: Cambridge University Press
Release Date : 1995-03-09

Affine Lie Algebras And Quantum Groups written by Jürgen Fuchs and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-03-09 with Mathematics categories.

This is an introduction to the theory of affine Lie Algebras, to the theory of quantum groups, and to the interrelationships between these two fields that are encountered in conformal field theory.

Factorizable Sheaves And Quantum Groups

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Author : Roman Bezrukavnikov
language : en
Publisher: Springer
Release Date : 2006-11-14

Factorizable Sheaves And Quantum Groups written by Roman Bezrukavnikov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

The book is devoted to the geometrical construction of the representations of Lusztig's small quantum groups at roots of unity. These representations are realized as some spaces of vanishing cycles of perverse sheaves over configuration spaces. As an application, the bundles of conformal blocks over the moduli spaces of curves are studied. The book is intended for specialists in group representations and algebraic geometry.