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.
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.