Quantum Groups and Their Primitive Ideals
by a more general quadratic algebra (possibly obtained by deformation) and then to derive Rq [G] by requiring it to possess the latter as a comodule. A third principle is to focus attention on the tensor structure of the cat egory of (!; modules. This means of course just defining an algebra struct...
| Main Author: | |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1995, 1995
|
| Edition: | 1st ed. 1995 |
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
|
| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 5.5 Comments and Complements
- 6. The Global Bases
- 6.1 The ? Operation and the Embedding Theorem
- 6.2 Globalization
- 6.3 The Demazure Property
- 6.4 Littelmann’s Path Crystals
- 6.5 Comments and Complements
- 7. Structure Theorems for Uq(g)
- 7.1 Local Finiteness for the Adjoint Action
- 7.2 Positivity of the Rosso Form
- 7.3 The Separation Theorem
- 7.4 Noetherianity
- 7.5 Comments and Complements
- 8. The Primitive Spectrum of Uq(g)
- 8.1 The Poincaré Series of the Harmonic Space
- 8.2 Factorization of the Quantum PRV Determinants
- 8.3 Verma Module Annihilators
- 8.4 Equivalence of Categories
- 8.5 Comments and Complements
- 9. Structure Theorems for Rq[G]
- 9.1 Commutativity Relations
- 9.2 Surjectivity and Injectivity Theorems
- 9.3 The Adjoint Action
- 9.4 The R-Matrix
- 9.5 Comments and Complements
- 10. The PrimeSpectrum of Rq[G]
- 10.1 Highest Weight Modules
- 10.2 The Quantum Weyl Group
- 10.3 Prime and Primitive Ideals of Rq[G]
- 10.4 Hopf Algebra Automorphisms
- 10.5 Comments and Complements
- A.2 Excerpts from Ring Theory
- A.3 Combinatorial Identities and Dimension Theory
- A.4 Remarks on Constructions of Quantum Groups
- A.5 Comments and Complements
- Index of Notation
- I. Hopf Algebras
- 1.1 Axioms of a Hopf Algebra
- 1.2 Group Algebras and Enveloping Algebras
- 1.3 Adjoint Action
- 1.4 The Hopf Dual
- 1.5 Comments and Complements
- 2. Excerpts from the Classical Theory
- 2.1 Lie Algebras
- 2.2 Algebraic Lie Algebras
- 2.3 Algebraic Groups
- 2.4 Lie Algebras of Algebraic Groups
- 2.5 Comments and Complements
- 3. Encoding the Cartan Matrix
- 3.1 Quantum Weyl Algebras
- 3.2 The Drinfeld Double
- 3.3 The Rosso Form and the Casimir Invariant
- 3.4 The Classical Limit and the Shapovalev Form
- 3.5 Comments and Complements
- 4. Highest Weight Modules
- 4.1 The Jantzen Filtration and Sum Formula
- 4.2 Kac-Moody Lie Algebras
- 4.3 Integrable Modules for Uq(gc)
- 4.4 Demazure Modules and Product Formulae
- 4.5 Comments and Complements
- 5. The Crystal Basis
- 5.1 Operators in the Crystal Limit
- 5.2 Crystals
- 5.3 Ad-invariant Filtrations, Twisted Actions and the Crystal Basis for Uq(n-)
- 5.4 The Grand Loop