Lectures on algebraic quantum groups / Ken A. Brown, Ken R. Goodearl.
Series 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 descriptionPreface 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] --
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode |
|---|---|---|---|---|---|---|---|
Libros
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Instituto de Matemática, CONICET-UNS | Últimas adquisiciones | 16 B877 (Browse shelf) | Available | A-9426 |
Includes bibliographical references (p. [331]-339) and index.
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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