LEADER 04763nam 2200613 450 001 9910788618803321 005 20170822144504.0 010 $a0-8218-9108-1 035 $a(CKB)3360000000464088 035 $a(EBL)3114441 035 $a(SSID)ssj0000888991 035 $a(PQKBManifestationID)11453160 035 $a(PQKBTitleCode)TC0000888991 035 $a(PQKBWorkID)10875998 035 $a(PQKB)10756585 035 $a(MiAaPQ)EBC3114441 035 $a(RPAM)17318775 035 $a(PPN)195419170 035 $a(EXLCZ)993360000000464088 100 $a20150416h20122012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aHopf algebras and congruence subgroups /$fYorck Sommerha?user, Yongchang Zhu 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2012. 210 4$dİ2012 215 $a1 online resource (134 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vVolume 219, Number 1028 300 $a"September 2012 , Volume 219, Number 1028 (first of 5 numbers)." 311 $a0-8218-6913-2 320 $aIncludes bibliographical references and index. 327 $a""Contents""; ""Abstract""; ""Introduction""; ""Chapter 1. The Modular Group""; ""1.1. Generators and relations""; ""1.2. Congruence subgroups""; ""1.3. Orbits and congruence relations""; ""1.4. Presentations of the reduced modular group""; ""Chapter 2. Quasitriangular Hopf Algebras""; ""2.1. Quasitriangular Hopf algebras""; ""2.2. The Drinfela???d double construction""; ""2.3. Integrals of the Drinfela???d double""; ""2.4. Twisting""; ""Chapter 3. Factorizable Hopf Algebras""; ""3.1. Doubles of quasitriangular Hopf algebras""; ""3.2. Factorizable Hopf algebras"" 327 $a""3.3. The coproduct of the evaluation form""""3.4. The double and the tensor product""; ""3.5. Integrals of factorizable Hopf algebras""; ""Chapter 4. The Action of the Modular Group""; ""4.1. The role of the integral""; ""4.2. The inverse of \ ""; ""4.3. Ribbon elements""; ""4.4. The linearity of the action""; ""4.5. Integrals, ribbon elements, and the double""; ""4.6. The modular group and the double""; ""Chapter 5. The Semisimple Case""; ""5.1. The character ring""; ""5.2. The Verlinde matrix""; ""5.3. Matrix identities""; ""5.4. A comparison""; ""5.5. The exponent"" 327 $a""5.6. Radforda???s example""""Chapter 6. The Case of the Drinfela???d Double""; ""6.1. The role of the evaluation form""; ""6.2. The new maps""; ""6.3. The first relation""; ""6.4. The second approach to the action of the modular group""; ""6.5. Matrix representations of the new maps""; ""Chapter 7. Induced Modules""; ""7.1. Induction""; ""7.2. Induction and duality""; ""7.3. The relation with the center construction""; ""7.4. The relation of the coherence properties""; ""7.5. Adjoint functors""; ""7.6. More coherence properties""; ""Chapter 8. Equivariant Frobenius-Schur Indicators"" 327 $a""8.1. Equivariant Frobenius-Schur indicators""""8.2. Indicators and duality""; ""8.3. The equivariance theorem""; ""8.4. The orbit theorem""; ""Chapter 9. Two Congruence Subgroup Theorems""; ""9.1. The action on the character ring""; ""9.2. Induction and multiplicities""; ""9.3. The congruence subgroup theorem for the Drinfela???d double""; ""9.4. The projective congruence subgroup theorem""; ""Chapter 10. The Action of the Galois Group""; ""10.1. The Galois group and the character ring""; ""10.2. The semilinear actions""; ""10.3. The action on the center"" 327 $a""10.4. Representations of the Drinfela???d double""""10.5. The equivariance of the isomorphism""; ""Chapter 11. Galois Groups and Indicators""; ""11.1. A digression on Frobenius algebras""; ""11.2. The invariance of the induced trivial module""; ""11.3. The action and the indicators""; ""11.4. Diagonal matrices""; ""11.5. The Galois group and the modular group""; ""Chapter 12. Galois Groups and Congruence Subgroups""; ""12.1. The Hopf symbol""; ""12.2. Properties of the Hopf symbol""; ""12.3. The Hopf symbol and the Jacobi symbol""; ""12.4. The linear congruence subgroup theorem""; ""Notes"" 327 $a""Bibliography"" 410 0$aMemoirs of the American Mathematical Society ;$vVolume 219, Number 1028. 606 $aHopf algebras 606 $aModular groups 615 0$aHopf algebras. 615 0$aModular groups. 676 $a512/.55 700 $aSommerha?user$b Yorck$f1966-$067460 702 $aZhu$b Yongchang 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910788618803321 996 $aHopf algebras and congruence subgroups$93743112 997 $aUNINA