Modern Birkhäuser Classics

Introduction to Quantum Groups

Authors: Lusztig, George

  • A classical introduction to quantum groups
  • Exercises and open problems included
  • The standard reference book for the material presented
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eBook $49.99
price for USA (gross)
  • ISBN 978-0-8176-4717-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $65.00
price for USA
  • ISBN 978-0-8176-4716-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo in 1985, or variations thereof. It is shown that these algebras have natural integral forms that can be specialized at roots of 1 and yield new objects, which include quantum versions of the semi-simple groups over fields of positive characteristic. The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of the theory are provided with canonical bases having rather remarkable properties. This book contains an extensive treatment of the theory of canonical bases in the framework of perverse sheaves. The theory developed in the book includes the case of quantum affine enveloping algebras and, more generally, the quantum analogs of the Kac–Moody Lie algebras.

Introduction to Quantum Groups will be of interest to mathematicians working in the representation theory of Lie groups and Lie algebras, knot theorists, theoretical physicists, and graduate students. Since large parts of the book are independent of the theory of perverse sheaves, the work may also be used as a textbook.

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There is no doubt that this volume is a very remarkable piece of work...Its appearance represents a landmark in the mathematical literature.

—Bulletin of the London Mathematical Society

This book is an important contribution to the field and can be recommended especially to mathematicians working in the field.

—EMS Newsletter

The present book gives a very efficient presentation of an important part of quantum group theory. It is a valuable contribution to the literature.

—Mededelingen van het Wiskundig

Lusztig's book is very well written and seems to be flawless...Obviously, this will be the standard reference book for the material presented and anyone interested in the Drinfeld–Jimbo algebras will have to study it very carefully.

—ZAA

[T]his book is much more than an 'introduction to quantum groups.' It contains a wealth of material. In addition to the many important results (of which several are new–at least in the generality presented here), there are plenty of useful calculations (commutator formulas, generalized quantum Serre relations, etc.).

—Zentralblatt MATH

Reviews

From the reviews:

"There is no doubt that this volume is a very remarkable piece of work...Its appearance represents a landmark in the mathematical literature."

—Bulletin of the London Mathematical Society

"This book is an important contribution to the field and can be recommended especially to mathematicians working in the field."

—EMS Newsletter

"The present book gives a very efficient presentation of an important part of quantum group theory. It is a valuable contribution to the literature."

—Mededelingen van het Wiskundig

"Lusztig's book is very well written and seems to be flawless...Obviously, this will be the standard reference book for the material presented and anyone interested in the Drinfeld–Jimbo algebras will have to study it very carefully."

—ZAA

"[T]his book is much more than an 'introduction to quantum groups.' It contains a wealth of material. In addition to the many important results (of which several are new–at least in the generality presented here), there are plenty of useful calculations (commutator formulas, generalized quantum Serre relations, etc.)."

—Zentralblatt MATH

“George Lusztig lays out the large scale structure of the discussion that follows in the 348 pages of his Introduction to Quantum Groups. … A significant and important work. … it’s terrific stuff, elegant and deep, and Lusztig presents it very well indeed, of course.” (Michael Berg, The Mathematical Association of America, January, 2011)


Table of contents (42 chapters)

  • The Algebra f

    Lusztig, George

    Pages 2-13

  • Weyl Group, Root Datum

    Lusztig, George

    Pages 14-18

  • The Algebra U

    Lusztig, George

    Pages 19-33

  • The Quasi- $$\mathcal{R}$$ -Matrix

    Lusztig, George

    Pages 34-39

  • The Symmetries $$T^{\prime}_{\rm {i, e}}, \ T^{\prime \prime}_{\rm {i, e}}$$ of an Integrable U-Module

    Lusztig, George

    Pages 40-47

Buy this book

eBook $49.99
price for USA (gross)
  • ISBN 978-0-8176-4717-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $65.00
price for USA
  • ISBN 978-0-8176-4716-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Introduction to Quantum Groups
Authors
Series Title
Modern Birkhäuser Classics
Copyright
2010
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-0-8176-4717-9
DOI
10.1007/978-0-8176-4717-9
Softcover ISBN
978-0-8176-4716-2
Series ISSN
2197-1803
Edition Number
1
Number of Pages
XIV, 352
Topics