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Lectures on Algebraic Quantum Groups Ken Brown

Lectures on Algebraic Quantum Groups By Ken Brown

Lectures on Algebraic Quantum Groups by Ken Brown

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Summary

This book consists of an expanded set of lectures on algebraic aspects of quantum groups. It particularly concentrates on quantized coordinate rings of algebraic groups and spaces and on quantized enveloping algebras of semisimple Lie algebras.

Lectures on Algebraic Quantum Groups Summary

Lectures on Algebraic Quantum Groups by Ken Brown

This book consists of an expanded set of lectures on algebraic aspects of quantum groups. It particularly concentrates on quantized coordinate rings of algebraic groups and spaces and on quantized enveloping algebras of semisimple Lie algebras. Large parts of the material are developed in full textbook style, featuring many examples and numerous exercises; other portions are discussed with sketches of proofs, while still other material is quoted without proof.

Lectures on Algebraic Quantum Groups Reviews

The proofs, sketches of proofs, and quotations from the literature are carefully written. Numerous examples and exercises are included, and bibliographical notes conclude each chapter. The second and third parts end with a discussion of open problems and perspectives for further research.

--Mathematical Reviews

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. Muller's Theorem and blocks.- III.10. Problems and perspectives.

Additional information

NLS9783764367145
9783764367145
3764367148
Lectures on Algebraic Quantum Groups by Ken Brown
Ken Brown
Advanced Courses in Mathematics - CRM Barcelona
New
Paperback
Birkhauser Verlag AG
2002-04-01
348
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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