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Lectures on algebraic quantum groups / Ken A. Brown, Ken R. Goodearl.

Por: Brown, Kenneth A. (Kenneth Alexander), 1951-Colaborador(es): Goodearl, K. RSeries Advanced courses in mathematics, CRM BarcelonaEditor: Basel ; Boston : Birkhäuser, c2002Descripción: ix, 348 p. : ill. ; 24 cmISBN: 3764367148 (pbk.)Tema(s): Quantum groups | Associative algebrasOtra clasificación: 16W35 (17B37 20G42 81R50) Recursos en línea: Publisher description
Contenidos incompletos:
Preface vii --
Part I. Background and Beginnings --
I.1. Beginnings and first examples [1] --
I.2. Further quantized coordinate rings [15] --
I.3. The quantized enveloping algebra of [25] --
I.4. The finite dimensional representations of [29] --
I.5. Primer on semisimple Lie algebras [39] --
I.6. Structure and representation theory of U (g)with g generic [45] --
I.7. Generic quantized coordinate rings of scmisimple groups [59] --
I.8. O(G) is a noetherian domain [69] --
Appendices to Part [1] --
I.9. Bialgebras and Hopf algebras [81] --
I.10. R-matrices [93] --
I.11. The Diamond Lemma [97] --
I.12. Filtered and graded rings [103] --
I.13. Polynomial identity algebras [113] --
I.14. Skew polynomial rings satisfying a polynomial identity [119] --
I.15. Homological conditions [125] --
I.16. Links and blocks [129] --
Part II Generic Quantized Coordinate Rings --
II. 1. The prime spectrum [135] --
II.2. Stratification [147] --
II. 3. Proof of the Stratification Theorem [159] --
II.4. Prime Ideate in [165] --
II.5 H-primes In iterated skew polynomial algebras [173] --
II. 6. More on iterated skew polynomial algebras [185] --
II. 7. The primitive spectrum [195] --
II.8. The Dixmier-Moaglin equivalence [205] --
II.9. Catenarity [215] --
II. 10. Problems and conjectures [229] --
Part III. Quantized algebras at Roots of Unity --
III. 1. Finite dimensional modules for affine PI algebras [237] --
III.2. The finite dimensional representations of [247] --
III.3. The finite dimensional representations of [255] --
III.4. Basic properties of PI Hopf triples [259] --
III.5. Poisson structures [273] --
III.6. Structure [281] --
III.7. Structure and representations of Oe(G) [289] --
III.8. Homological properties and the Azumaya locus [303] --
III. 9. Muller’s Theorem and blocks [313] --
III. 10. Problems and perspectives [323] --
--
Bibliography [331] --
Index [341] --
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