**Graduate Studies in Mathematics**

Volume: 22;
2000;
212 pp;
Hardcover

MSC: Primary 16; 17;
Secondary 13; 20

Print ISBN: 978-0-8218-0859-7

Product Code: GSM/22

List Price: $48.00

Individual Member Price: $38.40

**Electronic ISBN: 978-1-4704-2077-2
Product Code: GSM/22.E**

List Price: $48.00

Individual Member Price: $38.40

# Growth of Algebras and Gelfand-Kirillov Dimension: Revised Edition

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*Günter R. Krause; Thomas H. Lenagan*

During the two decades that preceded the publication of the first edition of
this book, the Gelfand-Kirillov dimension had emerged as a very useful and
powerful tool for investigating non-commutative algebras. At that time, the
basic ideas and results were scattered throughout various journal articles.
The first edition of this book provided a much-needed reliable and coherent
single source of information. Since that time, the book has become the standard
reference source for researchers.

For this edition, the authors incorporated the original text with only minor
modifications. Errors have been corrected, items have been rephrased, and more
mathematical expressions have been displayed for the purpose of clarity.

The newly added Chapter 12 provides broad overviews of the new
developments that have surfaced in the last few years, with references
to the literature for details. The bibliography has been updated and
accordingly, almost double the size of the original one.

The faithful revision and contemporary design of this work offers
time-honored expertise with modern functionality: A keenly appealing
combination. So, whether for the classroom, the well-tended
mathematical books collection, or the research desk, this book holds
unprecedented relevance.

#### Table of Contents

# Table of Contents

## Growth of Algebras and Gelfand-Kirillov Dimension: Revised Edition

- Cover Cover11 free
- Title v6 free
- Copyright vi7 free
- Contents vii8 free
- Preface ix10 free
- Introduction 112 free
- Chapter 1. Growth of Algebras 516 free
- Chapter 2. Gelfand-Kirillov Dimension of Algebras 1324
- Chapter 3. Gelfand-Kirillov Dimension of Related Algebras 2334
- Chapter 4. Localization 3748
- Chapter 5. Modules 5162
- Chapter 6. Graded and Filtered Algebras and Modules 6172
- Chapter 7. Almost Commutative Algebras 7384
- Chapter 8. Weyl Algebras 8798
- Chapter 9. Enveloping Algebras of Solvable Lie Algebras 109120
- Chapter 10. Polynomial Identity Algebras 125136
- Chapter 11. Growth of Groups 139150
- Chapter 12. New Developments 153164
- §12.1. Notes on Chapter 1 153164
- §12.2. Notes on Chapter 2 155166
- §12.3. Notes on Chapter 3 163174
- §12.4. Notes on Chapter 4 167178
- §12.5. Notes on Chapter 5 170181
- §12.6. Notes on Chapter 6 173184
- §12.7. Notes on Chapter 7 182193
- §12.8. Notes on Chapter 8 183194
- §12.9. Notes on Chapter 9 187198
- §12.10. Notes on Chapter 10 191202
- §12.11. Notes on Chapter 11 195206

- Bibliography 199210
- Index 209220
- Back Cover Back Cover1224

#### Readership

Advanced graduate students and research mathematicians interested in non-commutative algebra; mathematical physicists.

#### Reviews

Has become a standard reference on the Gelfand-Kirillov dimension … The new Chapter 12 … is of value because it is difficult to find it in the literature … This book is a good exposition of the subject and it may serve as an introduction to it as well. The presentation is clear and contains many complete proofs.

-- Zentralblatt MATH

The appearance of a second edition signals that the book is good and interesting. This is certainly the case with the monograph under review … it is very carefully and clearly written, and can be recommended not only to specialists, but to anybody who either intends to start working in this interesting field or needs some information concerning the Gelfand-Kirillov dimension … The book reads well, and the authors often mention the historical development of the subject and provide the text with many interesting examples.

-- European Mathematical Society Newsletter

The authors clearly had user-friendliness in mind in preparing this edition. Revisions have focused on clarification of presentation, the numbering of results from the original edition has been retained, and the new final chapter is organized so that Section 12.k gives updates relevant to Chapter k. The original bibliography has been expanded to about double its original length. This new edition will serve to continue to make this book a useful introduction to and reference in its field.

-- Mathematical Reviews