Author | Brown, Ken A. author |
---|---|
Title | Lectures on Algebraic Quantum Groups [electronic resource] / by Ken A. Brown, Ken R. Goodearl |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2002 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8205-7 |
Descript | IX, 348 p. 2 illus. online resource |
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. Mรผllerโs Theorem and blocks -- III.10. Problems and perspectives