Cohomology for quantum groups via the geometry of the nullcone / / Christopher P. Bendel [and three others]
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| Autore: |
Bendel Christopher P. <1969->
|
| Titolo: |
Cohomology for quantum groups via the geometry of the nullcone / / Christopher P. Bendel [and three others]
|
| Pubblicazione: | Providence, Rhode Island : , : American Mathematical Society, , 2013 |
| ©2013 | |
| Descrizione fisica: | 1 online resource (110 p.) |
| Disciplina: | 512/.55 |
| Soggetto topico: | Cohomology operations |
| Algebraic topology | |
| Persona (resp. second.): | BendelChristopher P. <1969-> |
| Note generali: | "Volume 229, Number 1077 (fourth of 5 numbers)." |
| Nota di bibliografia: | Includes bibliographical references. |
| Nota di contenuto: | ""Contents""; ""Introduction""; ""Chapter 1. Preliminaries and Statement of Results""; ""1.1. Some preliminary notation""; ""1.2. Main results""; ""Chapter 2. Quantum Groups, Actions, and Cohomology""; ""2.1. Listings""; ""2.2. Quantum enveloping algebras""; ""2.3. Connections with algebraic groups""; ""2.4. Root vectors and PBW-basis""; ""2.5. Levi and parabolic subalgebras""; ""2.6. The subalgebra _{ }( _{ })""; ""2.7. Adjoint action""; ""2.8. Finite dimensionality of cohomology groups""; ""2.9. Spectral sequences and the Euler characteristic""; ""2.10. Induction functors"" |
| ""Chapter 3. Computation of Î?â?€ and (Î?â?€)""""3.1. Subroot systems defined by weights""; ""3.2. The case of the classical Lie algebras""; ""3.3. The case of the exceptional Lie algebras""; ""3.4. Standardizing Î?â?€""; ""3.5. Resolution of singularities""; ""3.6. Normality of orbit closures""; ""Chapter 4. Combinatorics and the Steinberg Module""; ""4.1. Steinberg weights""; ""4.2. Weights of Î?^{â??}_{ , }""; ""4.3. Multiplicity of the Steinberg module""; ""4.4. Proof of Proposition 4.2.1""; ""4.5. The weight _{ }""; ""4.6. Types _{ }, _{ }, _{ }""; ""4.7. Type _{ }"" | |
| ""4.8. Type _{ } with dividing +1""""4.9. Exceptional Lie algebras""; ""Chapter 5. The Cohomology Algebra ^{â??}( _{ }( ),â??)""; ""5.1. Spectral sequences, I""; ""5.2. Spectral sequences, II""; ""5.3. An identification theorem""; ""5.4. Spectral sequences, III""; ""5.5. Proof of main result, Theorem 1.2.3, I""; ""5.6. Spectral sequences, IV""; ""5.7. Proof of the main result, Theorem 1.2.3, II""; ""Chapter 6. Finite Generation""; ""6.1. A finite generation result""; ""6.2. Proof of part (a) of Theorem 1.2.4""; ""6.3. Proof of part (b) of Theorem 1.2.4"" | |
| ""Chapter 7. Comparison with Positive Characteristic""""7.1. The setting""; ""7.2. Assumptions""; ""7.3. Consequences""; ""7.4. Special cases""; ""Chapter 8. Support Varieties over _{ } for the Modules â??_{ }( ) and Î?_{ }( )""; ""8.1. Quantum support varieties""; ""8.2. Lower bounds on the dimensions of support varieties""; ""8.3. Support varieties of â??_{ }( ): general results""; ""8.4. Support varieties of Î?_{ }( ) when is good""; ""8.5. A question of naturality of support varieties""; ""8.6. The Constrictor Method I""; ""8.7. The Constrictor Method II"" | |
| ""8.8. Support varieties of â??_{ }( ) when is bad""""8.9. â?? when 3\mid ""; ""8.10. â?? when 3\mid ""; ""8.11. â?? when 3\mid ""; ""8.12. â?? when 3\mid , 5\mid ""; ""8.13. Support varieties of Î?_{ }( ) when is bad""; ""Appendix A.""; ""A.1. Tables I""; ""A.2. Tables II""; ""Bibliography"" | |
| Titolo autorizzato: | Cohomology for quantum groups via the geometry of the nullcone |
| ISBN: | 1-4704-1531-3 |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910814572203321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
Memoirs of the American Mathematical Society ; ; Volume 229, Number 1077.