04619nam 2200613 450 991081457220332120170822144318.01-4704-1531-3(CKB)3710000000230214(EBL)3114224(SSID)ssj0001108985(PQKBManifestationID)11622326(PQKBTitleCode)TC0001108985(PQKBWorkID)11109317(PQKB)10774882(MiAaPQ)EBC3114224(RPAM)17984926(PPN)195408624(EXLCZ)99371000000023021420150417h20132013 uy 0engur|n|---|||||txtccrCohomology for quantum groups via the geometry of the nullcone /Christopher P. Bendel [and three others]Providence, Rhode Island :American Mathematical Society,2013.©20131 online resource (110 p.)Memoirs of the American Mathematical Society,1947-6221 ;Volume 229, Number 1077"Volume 229, Number 1077 (fourth of 5 numbers)."0-8218-9175-8 Includes bibliographical references.""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""Memoirs of the American Mathematical Society ;Volume 229, Number 1077.Cohomology operationsAlgebraic topologyCohomology operations.Algebraic topology.512/.55Bendel Christopher P.1969-1678285Bendel Christopher P.1969-American Mathematical Society.MiAaPQMiAaPQMiAaPQBOOK9910814572203321Cohomology for quantum groups via the geometry of the nullcone4045780UNINA