Cohomology for quantum groups via the geometry of the nullcone /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Bendel, Christopher P., 1969- (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence, Rhode Island : American Mathematical Society, 2013.
Colección:Memoirs of the American Mathematical Society ; Volume 229, no. 1077.
Temas:
Cohomology operations.
Algebraic topology.
Opérations cohomologiques.
Topologie algébrique.
Algebraic topology
Cohomology operations
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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""

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