Memoirs of the American Mathematical Society 1994; 67 pp; softcover Volume: 108 ISBN10: 0821825801 ISBN13: 9780821825808 List Price: US$34 Individual Members: US$20.40 Institutional Members: US$27.20 Order Code: MEMO/108/519
 This monograph will appeal to graduate students and researchers interested in Lie algebras. McGovern classifies the completely prime maximal spectrum of the enveloping algebra of any classical semisimple Lie algebra. He also studies finite algebra extensions of completely prime primitive quotients of such enveloping algebras and computes their lengths as bimodules, characteristic cycles, and Goldie ranks in many cases. This work marks a major advance in the quantization program, which seeks to extend the methods of (commutative) algebraic geometry to the setting of enveloping algebras. While such an extension cannot be completely carried out, this work shows that many partial results are available. Readership Research mathematicians in algebraic representation theory of semisimple Lie groups; advanced graduate students. Table of Contents  Introduction
 Preliminaries on nilpotent orbits and their covers
 Induced Dixmier algebras and orbit data
 Construction and basic properties of the algebras
 Associated varieties and characteristic cycles
 Goldie ranks
 Applications to the quantization program
 Exhaustion of the completely prime maximal spectrum
 Examples
 References
