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Growth of Algebras and Gelfand-Kirillov Dimension: Revised Edition
Günter R. Krause, University of Manitoba, Winnipeg, MB, Canada, and Thomas H. Lenagan, University of Edinburgh, Scotland

Graduate Studies in Mathematics
2000; 212 pp; hardcover
Volume: 22
ISBN-10: 0-8218-0859-1
ISBN-13: 978-0-8218-0859-7
List Price: US$48
Member Price: US$38.40
Order Code: GSM/22
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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.


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


"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

Table of Contents

  • Introduction
  • Growth of algebras
  • Gelfand-Kirillov dimension of algebras
  • Gelfand-Kirillov dimension of related algebras
  • Localization
  • Modules
  • Graded and filtered algebras and modules
  • Almost commutative algebras
  • Weyl algebras
  • Enveloping algebras of solvable Lie algebras
  • Polynomial identitiy algebras
  • Growth of groups
  • New developments
  • Bibliography
  • Index
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