LEADER 04619nam 2200613 450 001 9910814572203321 005 20170822144318.0 010 $a1-4704-1531-3 035 $a(CKB)3710000000230214 035 $a(EBL)3114224 035 $a(SSID)ssj0001108985 035 $a(PQKBManifestationID)11622326 035 $a(PQKBTitleCode)TC0001108985 035 $a(PQKBWorkID)11109317 035 $a(PQKB)10774882 035 $a(MiAaPQ)EBC3114224 035 $a(RPAM)17984926 035 $a(PPN)195408624 035 $a(EXLCZ)993710000000230214 100 $a20150417h20132013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aCohomology for quantum groups via the geometry of the nullcone /$fChristopher P. Bendel [and three others] 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2013. 210 4$dİ2013 215 $a1 online resource (110 p.) 225 1 $aMemoirs of the American Mathematical Society,$x1947-6221 ;$vVolume 229, Number 1077 300 $a"Volume 229, Number 1077 (fourth of 5 numbers)." 311 $a0-8218-9175-8 320 $aIncludes bibliographical references. 327 $a""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"" 327 $a""Chapter 3. Computation of I??a??? and (I??a???)""""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 I??a???""; ""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 I??^{a???}_{ , }""; ""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 _{ }"" 327 $a""4.8. Type _{ } with dividing +1""""4.9. Exceptional Lie algebras""; ""Chapter 5. The Cohomology Algebra ^{a???}( _{ }( ),a???)""; ""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"" 327 $a""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 a???_{ }( ) and I??_{ }( )""; ""8.1. Quantum support varieties""; ""8.2. Lower bounds on the dimensions of support varieties""; ""8.3. Support varieties of a???_{ }( ): general results""; ""8.4. Support varieties of I??_{ }( ) when is good""; ""8.5. A question of naturality of support varieties""; ""8.6. The Constrictor Method I""; ""8.7. The Constrictor Method II"" 327 $a""8.8. Support varieties of a???_{ }( ) when is bad""""8.9. a??? when 3\mid ""; ""8.10. a??? when 3\mid ""; ""8.11. a??? when 3\mid ""; ""8.12. a??? when 3\mid , 5\mid ""; ""8.13. Support varieties of I??_{ }( ) when is bad""; ""Appendix A.""; ""A.1. Tables I""; ""A.2. Tables II""; ""Bibliography"" 410 0$aMemoirs of the American Mathematical Society ;$vVolume 229, Number 1077. 606 $aCohomology operations 606 $aAlgebraic topology 615 0$aCohomology operations. 615 0$aAlgebraic topology. 676 $a512/.55 700 $aBendel$b Christopher P.$f1969-$01678285 702 $aBendel$b Christopher P.$f1969- 712 02$aAmerican Mathematical Society. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910814572203321 996 $aCohomology for quantum groups via the geometry of the nullcone$94045780 997 $aUNINA