04763nam 2200613 450 991078861880332120170822144504.00-8218-9108-1(CKB)3360000000464088(EBL)3114441(SSID)ssj0000888991(PQKBManifestationID)11453160(PQKBTitleCode)TC0000888991(PQKBWorkID)10875998(PQKB)10756585(MiAaPQ)EBC3114441(RPAM)17318775(PPN)195419170(EXLCZ)99336000000046408820150416h20122012 uy 0engur|n|---|||||txtccrHopf algebras and congruence subgroups /Yorck Sommerhäuser, Yongchang ZhuProvidence, Rhode Island :American Mathematical Society,2012.©20121 online resource (134 p.)Memoirs of the American Mathematical Society,0065-9266 ;Volume 219, Number 1028"September 2012 , Volume 219, Number 1028 (first of 5 numbers)."0-8218-6913-2 Includes bibliographical references and index.""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 Drinfelâ€?d double construction""; ""2.3. Integrals of the Drinfelâ€?d double""; ""2.4. Twisting""; ""Chapter 3. Factorizable Hopf Algebras""; ""3.1. Doubles of quasitriangular Hopf algebras""; ""3.2. Factorizable Hopf algebras""""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""""5.6. Radfordâ€?s example""""Chapter 6. The Case of the Drinfelâ€?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""""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 Drinfelâ€?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""""10.4. Representations of the Drinfelâ€?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""""Bibliography""Memoirs of the American Mathematical Society ;Volume 219, Number 1028.Hopf algebrasModular groupsHopf algebras.Modular groups.512/.55Sommerhäuser Yorck1966-67460Zhu YongchangMiAaPQMiAaPQMiAaPQBOOK9910788618803321Hopf algebras and congruence subgroups3743112UNINA