| Dewey Class |
512.2 |
| Title |
Introduction to Quantum Groups ([Ebook]) / by George Lusztig. |
| Author |
Lusztig, George, , 1946- |
| Other name(s) |
SpringerLink (Online service) |
| Publication |
Boston : Birkhäuser , 2010. |
| Physical Details |
XIV, 346 pages : online resource. |
| Series |
Modern Birkhäuser classics |
| ISBN |
9780817647179 |
| Summary Note |
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.There is no doubt that this volume is a very remarkable piece of work...Its appearance represents a landmark in the mathematical literature. âBulletin 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. âEMS 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. âMededelingen 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. âZAA [T]his book is much more than an: |
| Contents note |
Preface -- Part I: The Drinfeld-Jimbo Algebra U -- Part II: Geometric Realization of f -- Part III: Kashiwaraâs Operators and Applications -- Part IV: Canonical Basis of U -- Part V: Change of Rings -- Part VI: Braid Group Action -- Index of Notation -- Index of Terminology. |
| System details note |
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users) |
| Internet Site |
http://dx.doi.org/10.1007/978-0-8176-4717-9 |
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