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.

Readership

Graduate students and research mathematicians interested in Lie algebras.