Lectures on algebraic quantum groups /
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| Author / Creator: | BROWN, KEN A. |
|---|---|
| Imprint: | Basel ; Boston : Birkhàˆuser, 2002. |
| Description: | ix, 348 p. : ill. ; 24 cm. |
| Language: | English |
| Series: | Advanced courses in mathematics, CRM Barcelona |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/4712970 |
Table of Contents:
- Pt. I. Background and Beginnings
- I.1. Beginnings and first examples
- I.2. Further quantized coordinate rings
- I.3. The quantized enveloping algebra of sl[subscript 2](k)
- I.4. The finite dimensional representations of U[subscript q](sl[subscript 2](k))
- I.5. Primer on semisimple Lie algebras
- I.6. Structure and representation theory of U[subscript q](g) with q generic
- I.7. Generic quantized coordinate rings of semisimple groups
- I.8. O[subscript q](G) is a noetherian domain
- I.9. Bialgebras and Hopf algebras
- I.10. R-matrices
- I.11. The Diamond Lemma
- I.12. Filtered and graded rings
- I.13. Polynomial identity algebras
- I.14. Skew polynomial rings satisfying a polynomial identity
- I.15. Homological conditions
- I.16. Links and blocks
- Pt. II. Generic Qantized Coordinate Rings
- II.1. The prime spectrum
- II.2. Stratification
- II.3. Proof of the Stratification Theorem
- II.4. Prime ideals in O[subscript q](G)
- II.5. H-primes in iterated skew polynomial algebras
- II.6. More on iterated skew polynomial algebras
- II.7. The primitive spectrum
- II.8. The Dixmier-Moeglin equivalence
- II.9. Catenarity
- II.10. Problems and conjectures
- Pt. III. Quantized algebras at Roots of Unity
- III.1. Finite dimensional modules for affine PI algebras
- III.2. The finite dimensional representations of U[subscript [epsilon]](sl[subscript 2](k))
- III.3. The finite dimensional representations of O[subscript [epsilon]](SL[subscript 2](k))
- III.4. Basic properties of PI Hopf triples
- III.5. Poisson structures
- III.6. Structure of U[subscript [epsilon]](g)
- III.7. Structure and representations of O[subscript [epsilon]](G)
- III.8. Homological properties and the Azumaya locus
- III.9. Muller's Theorem and blocks
- III.10. Problems and perspectives.
