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Lectures on Algebraic Quantum Groups

In September 2000, at the Centre de Recerca Matematica in Barcelona, we pre­ sented a 30-hour Advanced Course on Algebraic Quantum Groups. After the course, we expanded and smoothed out the material presented in the lectures and inte­ grated it with the background material that we had prepared for t...

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Bibliographic Details
Main Authors: Brown, Ken, Goodearl, Ken R. (Author)
Format: eBook
Language:English
Published: Basel Birkhäuser Basel 2002, 2002
Edition:1st ed. 2002
Series:Advanced Courses in Mathematics - CRM Barcelona
Subjects:
Group Theory
Topological Groups, Lie Groups
Lie Groups
Topological Groups
Group Theory And Generalizations
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • Preface
  • I. BACKGROUND AND BEGINNINGS
  • I.1. Beginnings and first examples
  • I.2. Further quantized coordinate rings
  • I.3. The quantized enveloping algebra of sC2(k)
  • I.4. The finite dimensional representations of Uq(5r2(k))
  • I.5. Primer on semisimple Lie algebras
  • I.6. Structure and representation theory of Uq(g) with q generic
  • I.7. Generic quantized coordinate rings of semisimple groups
  • I.8. 0q(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
  • II. GENERIC QUANTIZED COORDINATE RINGS
  • II.1. The prime spectrum
  • II.2. Stratification
  • II.3. Proof of the Stratification Theorem
  • II.4. Prime ideals in 0q (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
  • III. QUANTIZED ALGEBRAS AT ROOTS OF UNITY
  • III.1. Finite dimensional modules for affine PI algebras
  • 1II.2. The finite dimensional representations of UE(5C2(k))
  • II1.3. The finite dimensional representations of OE(SL2(k))
  • III.4. Basic properties of PI Hopf triples
  • III.5. Poisson structures
  • 1II.6. Structure of U, (g)
  • III.7. Structure and representations of 0,(G)
  • III.8. Homological properties and the Azumaya locus
  • II1.9. Müller’s Theorem and blocks
  • III.10. Problems and perspectives

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