On the Spectra of Quantum Groups.
- 1st ed.
- 1 online resource (104 pages)
- Memoirs of the American Mathematical Society ; v.229 .
- Memoirs of the American Mathematical Society .
Intro -- Contents -- Chapter 1. Introduction -- Chapter 2. Previous results on spectra of quantum function algebras -- 2.1. Quantized universal enveloping algebras -- 2.2. Type 1 modules and braid group action -- 2.3. -prime ideals of Quantum Groups -- 2.4. Sets of normal elements -- 2.5. Localizations of quotients of _[ ] by its -primes -- 2.6. Spectral decomposition theorem for _[ ] -- 2.7. The De Concini-Kac-Procesi algebras -- 2.8. A second presentation of ^_ -- Chapter 3. A description of the centers of Joseph's localizations -- 3.1. Statement of the main result -- 3.2. Associated root and weight spaces -- 3.3. One side inclusion in \thref -- 3.4. Joseph's description of _ -- 3.5. Homogeneous -normal elements of the algebras ^_} -- 3.6. Homogeneous -normal elements of the algebras _ -- 3.7. Proof of \thref -- Chapter 4. Primitive ideals of _[ ] and a Dixmier map for _[ ] -- 4.1. A formula for the primitive ideals of _[ ] -- 4.2. Structure of _ _[ ] as a ^× ^-homogeneous space -- 4.3. The standard Poisson Lie structure on and its symplectic leaves -- 4.4. Equations for the symplectic leaves of ( ^, _) -- 4.5. A ^× ^-equivariant Dixmier map for ℝ_[ ] -- Chapter 5. Separation of variables for the algebras ^_ -- 5.1. Statement of the freeness result -- 5.2. Leading terms of the normal elements _^( ^_) -- 5.3. Proof of \thref -- Chapter 6. A classification of the normal and prime elements of the De Concini-Kac-Procesi algebras -- 6.1. Statement of the classification result -- 6.2. Homogeneous normal and -normal elements of ^_ -- 6.3. A lemma on diagonal automorphisms of ^_ -- 6.4. Proof of \prref. 6.5. Proof of \thref -- 6.6. Prime and primitive ideals in the -stratum of ^_. -- 6.7. A classification of the prime elements of ^_ -- Chapter 7. Module structure of _ over their subalgebras generated by Joseph's normal elements -- 7.1. Statement of the freeness result -- 7.2. A × -filtration of _ -- 7.3. The action of '_ on _ -- 7.4. Structure of the algebras '_ and separation of variables for _ -- 7.5. Structure of the algebras _ and freeness of _ over _ -- Chapter 8. A classification of maximal ideals of _[ ] and a question of Goodearl and Zhang -- 8.1. A projection property of the ideal _ -- 8.2. Proof of \prref -- 8.3. Proof of \thref -- 8.4. Classification of _[ ] and a question of Goodearl and Zhang -- Chapter 9. Chain properties and homological applications -- 9.1. Applications -- 9.2. ⁺⊛ ⁻ is an algebra with enough normal elements. -- Bibliography.