**Memoirs of the American Mathematical Society**

1994;
67 pp;
Softcover

MSC: Primary 17;
Secondary 20; 22

Print ISBN: 978-0-8218-2580-8

Product Code: MEMO/108/519

List Price: $36.00

Individual Member Price: $21.60

**Electronic ISBN: 978-1-4704-0096-5
Product Code: MEMO/108/519.E**

List Price: $36.00

Individual Member Price: $21.60

# Completely Prime Maximal Ideals and Quantization

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*William M. McGovern*

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.

#### Table of Contents

# Table of Contents

## Completely Prime Maximal Ideals and Quantization

- Contents vii8 free
- Chapter 1. Introduction 110 free
- Chapter 2. Preliminaries on Nilpotent Orbits and Their Covers 413 free
- Chapter 3. Induced Dixmier Algebras and Orbit Data 1019
- Chapter 4. Construction and Basic Properties of the Algebras 1928
- Chapter 5. Associated Varieties and Characteristic Cycles 2534
- Chapter 6. Goldie Ranks 3544
- Chapter 7. Applications to the Quantization Program 4655
- Chapter 8. Exhaustion of the Completely Prime Maximal Spectrum 5564
- Chapter 9. Examples 5867
- References 6473

#### Readership

Research mathematicians in algebraic representation theory of semisimple Lie groups; advanced graduate students.