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. It can be an excellent textbook for a graduate course, as well as a very useful source of references in the theory of universal enveloping algebras, the area of mathematics that remains as important today as it was 20 years ago.

For the 1996 printing, the author updated the status of open problems and added some relevant references.

Readership

Graduate students and research mathematicians interested in Lie algebras.

Reviews

"For the graduate student, this is a masterpiece of pedagogical writing, being succinct, wonderfully self-contained and of exceptional precision."

-- Mathematical Reviews

"Self-contained, written with precision and elegance ... an excellent textbook for the graduate student, a very good background for the professional algebraist not very familiar with the subject and a very useful source of references for the expert."

-- Zentralblatt MATH

Table of Contents

• Lie algebras
• Enveloping algebras
• Two-sided ideals in enveloping algebras
• Centres
• Induced representations
• Primitive ideas (The solvable case)
• Verma modules
• The enveloping algebra of a semi-simple Lie algebra
• Harish-Chandra modules
• Primitive ideals (The general case)
• Appendix
• Problems
• Bibliography
• Supplementary bibliography
• Added in 1996
• Subject index