Introduction to Quantum Groups
(Sprache: Englisch)
This book discusses quantized enveloping algebras (or variations thereof) introduced by Drinfeld and Jimbo. Coverage includes the case of quantum affine enveloping algebras and, more generally, the quantum analogs of the Kac Moody Lie algebras.
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Produktinformationen zu „Introduction to Quantum Groups “
This book discusses quantized enveloping algebras (or variations thereof) introduced by Drinfeld and Jimbo. Coverage includes the case of quantum affine enveloping algebras and, more generally, the quantum analogs of the Kac Moody Lie algebras.
Klappentext zu „Introduction to Quantum Groups “
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.
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 which 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 basis with rather remarkable properties. The 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.
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.
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.
Inhaltsverzeichnis zu „Introduction to Quantum Groups “
- Preface- The Drinfeld-Jimbo Algebra U
- Geometric Realization of f
- Part III. Kashiwara's Operators and Applications
- Canonical Basis of U
- Change of Rings
- Braid Group Action
- Index of Notation
- Index of Terminology
Bibliographische Angaben
- Autor: George Lusztig
- 2008, Pr., 352 Seiten, Maße: 15,9 x 23,3 cm, Kartoniert (TB), Englisch
- Verlag: Springer
- ISBN-10: 0817647163
- ISBN-13: 9780817647162
Sprache:
Englisch
Rezension zu „Introduction to Quantum Groups “
"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
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