Enveloping Algebras / Edition 1

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More About This Textbook

Overview

For the graduate student, this is a masterpiece of pedagogical writing, being succinct, wonderfully self-contained and of exceptional precision. —Mathematical Reviews This book, which is the first systematic exposition of the algebraic approach to representations of Lie groups via representations of (or modules over) the corresponding universal enveloping algebras, turned out to be so well written that even today it remains one of the main textbooks and reference books on the subject. In 1992, Jacques Dixmier was awarded the Leroy P. Steele Prize for expository writing in mathematics. The Committee's citation mentioned Enveloping Algebras as one of Dixmier's ''extraordinary books''. Written with unique precision and elegance, the book provides the reader with insight and understanding of this very important subject. For the 1996 printing, Dixmier updated the status of open problems and added some relevant references. The book is suitable as a textbook for a graduate course on enveloping algebras. It is also a valuable reference for graduate students and research mathematicians interested in Lie algebras.

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Editorial Reviews

Booknews
A classic graduate textbook and reference, originally published as Algebres enveloppantes. Provides a systematic exposition of the algebraic approach to representations of Lie groups via representations of the corresponding universal enveloping algebras. Assumes a general knowledge of Lie groups, and outlines the specific aspects needed. The 1996 reprint updates the status of open problems and adds a couple pages of bibliographic references. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780821805602
  • Publisher: American Mathematical Society
  • Publication date: 6/1/1996
  • Series: Graduate Studies in Mathematics Series , #11
  • Edition number: 1
  • Pages: 379
  • Product dimensions: 7.28 (w) x 10.04 (h) x 1.02 (d)

Table of Contents

Preface
Preface to the English edition
Notation
Ch. 1 Lie Algebras 1
Ch. 2 Enveloping Algebras 66
Ch. 3 Two Sided Ideals in Enveloping Algebras 101
Ch. 4 Centres 131
Ch. 5 Induced Representations 169
Ch. 6 Primitive Ideals (The Solvable Case) 192
Ch. 7 Verma Modules 231
Ch. 8 The Enveloping Algebra of a Semi-simple Lie Algebra 277
Ch. 9 Harish-Chandra Modules 295
Ch. 10 Primitive Ideals (The General Case) 325
Ch. 11 Appendix 346
Problems 354
Bibliography 359
Supplementary Bibliography 366
Added in 1996 371
Subject Index 375
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