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Hopf algebras and congruence subgroups / / Yorck Sommerhäuser, Yongchang Zhu
Hopf algebras and congruence subgroups / / Yorck Sommerhäuser, Yongchang Zhu
Autore Sommerhäuser Yorck <1966->
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , 2012
Descrizione fisica 1 online resource (134 p.)
Disciplina 512/.55
Collana Memoirs of the American Mathematical Society
Soggetto topico Hopf algebras
Modular groups
Soggetto genere / forma Electronic books.
ISBN 0-8218-9108-1
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""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 Drinfel�d double construction""; ""2.3. Integrals of the Drinfel�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. Radford�s example""""Chapter 6. The Case of the Drinfel�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 Drinfel�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 Drinfel�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""
Record Nr. UNINA-9910480527203321
Sommerhäuser Yorck <1966->  
Providence, Rhode Island : , : American Mathematical Society, , 2012
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Hopf algebras and congruence subgroups / / Yorck Sommerhäuser, Yongchang Zhu
Hopf algebras and congruence subgroups / / Yorck Sommerhäuser, Yongchang Zhu
Autore Sommerhäuser Yorck <1966->
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , 2012
Descrizione fisica 1 online resource (134 p.)
Disciplina 512/.55
Collana Memoirs of the American Mathematical Society
Soggetto topico Hopf algebras
Modular groups
ISBN 0-8218-9108-1
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""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 Drinfel�d double construction""; ""2.3. Integrals of the Drinfel�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. Radford�s example""""Chapter 6. The Case of the Drinfel�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 Drinfel�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 Drinfel�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""
Record Nr. UNINA-9910788618803321
Sommerhäuser Yorck <1966->  
Providence, Rhode Island : , : American Mathematical Society, , 2012
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Hopf algebras and congruence subgroups / / Yorck Sommerhäuser, Yongchang Zhu
Hopf algebras and congruence subgroups / / Yorck Sommerhäuser, Yongchang Zhu
Autore Sommerhäuser Yorck <1966->
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , 2012
Descrizione fisica 1 online resource (134 p.)
Disciplina 512/.55
Collana Memoirs of the American Mathematical Society
Soggetto topico Hopf algebras
Modular groups
ISBN 0-8218-9108-1
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""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 Drinfel�d double construction""; ""2.3. Integrals of the Drinfel�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. Radford�s example""""Chapter 6. The Case of the Drinfel�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 Drinfel�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 Drinfel�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""
Record Nr. UNINA-9910827428103321
Sommerhäuser Yorck <1966->  
Providence, Rhode Island : , : American Mathematical Society, , 2012
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
On higher Frobenius-Schur indicators / / Yevgenia Kashina, Yorck Sommerhäuser, Yongchang Zhu
On higher Frobenius-Schur indicators / / Yevgenia Kashina, Yorck Sommerhäuser, Yongchang Zhu
Autore Kashina Yevgenia <1971->
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , [2006]
Descrizione fisica 1 online resource (82 p.)
Disciplina 510 s
512/.55
Collana Memoirs of the American Mathematical Society
Soggetto topico Hopf algebras
Lie superalgebras
Frobenius algebras
Cauchy integrals
Soggetto genere / forma Electronic books.
ISBN 1-4704-0459-1
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""Contents""; ""Introduction""; ""Chapter 1. The Calculus of Sweedler Powers""; ""1.1. Monotone maps""; ""1.2. The union of the symmetric groups""; ""1.3. Bialgebras""; ""1.4. A monoid""; ""1.5. Permutations from sequences""; ""1.6. Sweedler powers""; ""Chapter 2. Frobenius-Schur Indicators""; ""2.1. Central Sweedler powers""; ""2.2. The coproduct of the Sweedler powers""; ""2.3. The first formula for the Frobenius-Schur indicators""; ""2.4. The Frobenius-Schur theorem""; ""2.5. Frobenius-Schur indicators of the regular representation""; ""Chapter 3. The Exponent""; ""3.1. The exponent""
""3.2. The second formula for the Frobenius-Schur indicators""""3.3. Sweedler powers of the integral""; ""3.4. Cauchy's theorem""; ""Chapter 4. The Order""; ""4.1. Order and multiplicity""; ""4.2. The divisibility theorem""; ""4.3. An example""; ""4.4. The dimension of the simple modules""; ""Chapter 5. The Index""; ""5.1. Indecomposable matrices""; ""5.2. The normal form""; ""5.3. The Perron-Frobenius theorem""; ""5.4. The index formula""; ""Chapter 6. The Drinfel'd Double""; ""6.1. The Drinfel'd double""; ""6.2. Factorizability""; ""6.3. The center of the character ring""
""6.4. The third formula for the Frobenius-Schur indicators""""Chapter 7. Examples""; ""7.1. A class of extensions""; ""7.2. The coefficients""; ""7.3. Sweedler powers of the integral""; ""7.4. The simple modules""; ""7.5. Nonintegral indicators""; ""7.6. Noncocommutative Sweedler powers""; ""7.7. Noncentral Sweedler powers""; ""Bibliography""; ""Subject Index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""L""; ""M""; ""N""; ""O""; ""P""; ""R""; ""S""; ""T""; ""U""; ""V""; ""W""; ""Symbol Index""
Record Nr. UNINA-9910479856303321
Kashina Yevgenia <1971->  
Providence, Rhode Island : , : American Mathematical Society, , [2006]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
On higher Frobenius-Schur indicators / / Yevgenia Kashina, Yorck Sommerhäuser, Yongchang Zhu
On higher Frobenius-Schur indicators / / Yevgenia Kashina, Yorck Sommerhäuser, Yongchang Zhu
Autore Kashina Yevgenia <1971->
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , [2006]
Descrizione fisica 1 online resource (82 p.)
Disciplina 510 s
512/.55
Collana Memoirs of the American Mathematical Society
Soggetto topico Hopf algebras
Lie superalgebras
Frobenius algebras
Cauchy integrals
ISBN 1-4704-0459-1
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""Contents""; ""Introduction""; ""Chapter 1. The Calculus of Sweedler Powers""; ""1.1. Monotone maps""; ""1.2. The union of the symmetric groups""; ""1.3. Bialgebras""; ""1.4. A monoid""; ""1.5. Permutations from sequences""; ""1.6. Sweedler powers""; ""Chapter 2. Frobenius-Schur Indicators""; ""2.1. Central Sweedler powers""; ""2.2. The coproduct of the Sweedler powers""; ""2.3. The first formula for the Frobenius-Schur indicators""; ""2.4. The Frobenius-Schur theorem""; ""2.5. Frobenius-Schur indicators of the regular representation""; ""Chapter 3. The Exponent""; ""3.1. The exponent""
""3.2. The second formula for the Frobenius-Schur indicators""""3.3. Sweedler powers of the integral""; ""3.4. Cauchy's theorem""; ""Chapter 4. The Order""; ""4.1. Order and multiplicity""; ""4.2. The divisibility theorem""; ""4.3. An example""; ""4.4. The dimension of the simple modules""; ""Chapter 5. The Index""; ""5.1. Indecomposable matrices""; ""5.2. The normal form""; ""5.3. The Perron-Frobenius theorem""; ""5.4. The index formula""; ""Chapter 6. The Drinfel'd Double""; ""6.1. The Drinfel'd double""; ""6.2. Factorizability""; ""6.3. The center of the character ring""
""6.4. The third formula for the Frobenius-Schur indicators""""Chapter 7. Examples""; ""7.1. A class of extensions""; ""7.2. The coefficients""; ""7.3. Sweedler powers of the integral""; ""7.4. The simple modules""; ""7.5. Nonintegral indicators""; ""7.6. Noncocommutative Sweedler powers""; ""7.7. Noncentral Sweedler powers""; ""Bibliography""; ""Subject Index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""L""; ""M""; ""N""; ""O""; ""P""; ""R""; ""S""; ""T""; ""U""; ""V""; ""W""; ""Symbol Index""
Record Nr. UNINA-9910788741803321
Kashina Yevgenia <1971->  
Providence, Rhode Island : , : American Mathematical Society, , [2006]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
On higher Frobenius-Schur indicators / / Yevgenia Kashina, Yorck Sommerhäuser, Yongchang Zhu
On higher Frobenius-Schur indicators / / Yevgenia Kashina, Yorck Sommerhäuser, Yongchang Zhu
Autore Kashina Yevgenia <1971->
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , [2006]
Descrizione fisica 1 online resource (82 p.)
Disciplina 510 s
512/.55
Collana Memoirs of the American Mathematical Society
Soggetto topico Hopf algebras
Lie superalgebras
Frobenius algebras
Cauchy integrals
ISBN 1-4704-0459-1
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""Contents""; ""Introduction""; ""Chapter 1. The Calculus of Sweedler Powers""; ""1.1. Monotone maps""; ""1.2. The union of the symmetric groups""; ""1.3. Bialgebras""; ""1.4. A monoid""; ""1.5. Permutations from sequences""; ""1.6. Sweedler powers""; ""Chapter 2. Frobenius-Schur Indicators""; ""2.1. Central Sweedler powers""; ""2.2. The coproduct of the Sweedler powers""; ""2.3. The first formula for the Frobenius-Schur indicators""; ""2.4. The Frobenius-Schur theorem""; ""2.5. Frobenius-Schur indicators of the regular representation""; ""Chapter 3. The Exponent""; ""3.1. The exponent""
""3.2. The second formula for the Frobenius-Schur indicators""""3.3. Sweedler powers of the integral""; ""3.4. Cauchy's theorem""; ""Chapter 4. The Order""; ""4.1. Order and multiplicity""; ""4.2. The divisibility theorem""; ""4.3. An example""; ""4.4. The dimension of the simple modules""; ""Chapter 5. The Index""; ""5.1. Indecomposable matrices""; ""5.2. The normal form""; ""5.3. The Perron-Frobenius theorem""; ""5.4. The index formula""; ""Chapter 6. The Drinfel'd Double""; ""6.1. The Drinfel'd double""; ""6.2. Factorizability""; ""6.3. The center of the character ring""
""6.4. The third formula for the Frobenius-Schur indicators""""Chapter 7. Examples""; ""7.1. A class of extensions""; ""7.2. The coefficients""; ""7.3. Sweedler powers of the integral""; ""7.4. The simple modules""; ""7.5. Nonintegral indicators""; ""7.6. Noncocommutative Sweedler powers""; ""7.7. Noncentral Sweedler powers""; ""Bibliography""; ""Subject Index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""L""; ""M""; ""N""; ""O""; ""P""; ""R""; ""S""; ""T""; ""U""; ""V""; ""W""; ""Symbol Index""
Record Nr. UNINA-9910812417003321
Kashina Yevgenia <1971->  
Providence, Rhode Island : , : American Mathematical Society, , [2006]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui