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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
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
Hopf algebras and Galois theory / / Stephen U. Chase, Moss E. Sweedler
Hopf algebras and Galois theory / / Stephen U. Chase, Moss E. Sweedler
Autore Chase Stephen U (Stephen Urban), <1932->
Edizione [1st ed. 1969.]
Pubbl/distr/stampa Berlin, Germany ; ; New York, New York : , : Springer-Verlag, , [1969]
Descrizione fisica 1 online resource (IV, 140 p.)
Disciplina 512.82
Collana Lecture Notes in Mathematics
Soggetto topico Hopf algebras
Galois theory
ISBN 3-540-36134-0
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Galois objects -- Hopf algebras and galois theory -- Galois objects and extensions of Hopf algebras.
Record Nr. UNISA-996466638203316
Chase Stephen U (Stephen Urban), <1932->  
Berlin, Germany ; ; New York, New York : , : Springer-Verlag, , [1969]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Hopf algebras and generalizations : AMS Special Session on Hopf Algebras at the Crossroads of Algebra, Category Theory, and Topology, October 23-24, 2004, Evanston, Illinois / / Louis H. Kauffman, David E. Radford, Fernando J.O. Souza, editors
Hopf algebras and generalizations : AMS Special Session on Hopf Algebras at the Crossroads of Algebra, Category Theory, and Topology, October 23-24, 2004, Evanston, Illinois / / Louis H. Kauffman, David E. Radford, Fernando J.O. Souza, editors
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , [2007]
Descrizione fisica 1 online resource (186 p.)
Disciplina 512/.55
Collana Contemporary mathematics
Soggetto topico Hopf algebras
Soggetto genere / forma Electronic books.
ISBN 0-8218-8120-5
0-8218-3820-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""Contents""; ""Preface""; ""Lax Braidings and the Lax Centre""; ""Dynamical Quantum Groups - The Super Story""; ""Groups of Grouplike Elements of a Semisimple Hopf Algebra and Its Dual""; ""Higher Frobenius-Schur Indicators for Pivotal Structures""; ""Doubles of (quasi) Hopf Algebras and Some Examples of Quantum Groupoids and Vertex Groups Related to Them""; ""Central Braided Hopf Algebras""; ""A Note on Anti-Yetter-Drinfeld Modules""; ""Representations of the Hopf Algebra U(n)""
Record Nr. UNINA-9910480980603321
Providence, Rhode Island : , : American Mathematical Society, , [2007]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Hopf algebras and generalizations : AMS Special Session on Hopf Algebras at the Crossroads of Algebra, Category Theory, and Topology, October 23-24, 2004, Evanston, Illinois / / Louis H. Kauffman, David E. Radford, Fernando J.O. Souza, editors
Hopf algebras and generalizations : AMS Special Session on Hopf Algebras at the Crossroads of Algebra, Category Theory, and Topology, October 23-24, 2004, Evanston, Illinois / / Louis H. Kauffman, David E. Radford, Fernando J.O. Souza, editors
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , [2007]
Descrizione fisica 1 online resource (186 p.)
Disciplina 512/.55
Collana Contemporary mathematics
Soggetto topico Hopf algebras
ISBN 0-8218-8120-5
0-8218-3820-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""Contents""; ""Preface""; ""Lax Braidings and the Lax Centre""; ""Dynamical Quantum Groups - The Super Story""; ""Groups of Grouplike Elements of a Semisimple Hopf Algebra and Its Dual""; ""Higher Frobenius-Schur Indicators for Pivotal Structures""; ""Doubles of (quasi) Hopf Algebras and Some Examples of Quantum Groupoids and Vertex Groups Related to Them""; ""Central Braided Hopf Algebras""; ""A Note on Anti-Yetter-Drinfeld Modules""; ""Representations of the Hopf Algebra U(n)""
Record Nr. UNINA-9910788792103321
Providence, Rhode Island : , : American Mathematical Society, , [2007]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Hopf algebras and generalizations : AMS Special Session on Hopf Algebras at the Crossroads of Algebra, Category Theory, and Topology, October 23-24, 2004, Evanston, Illinois / / Louis H. Kauffman, David E. Radford, Fernando J.O. Souza, editors
Hopf algebras and generalizations : AMS Special Session on Hopf Algebras at the Crossroads of Algebra, Category Theory, and Topology, October 23-24, 2004, Evanston, Illinois / / Louis H. Kauffman, David E. Radford, Fernando J.O. Souza, editors
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , [2007]
Descrizione fisica 1 online resource (186 p.)
Disciplina 512/.55
Collana Contemporary mathematics
Soggetto topico Hopf algebras
ISBN 0-8218-8120-5
0-8218-3820-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""Contents""; ""Preface""; ""Lax Braidings and the Lax Centre""; ""Dynamical Quantum Groups - The Super Story""; ""Groups of Grouplike Elements of a Semisimple Hopf Algebra and Its Dual""; ""Higher Frobenius-Schur Indicators for Pivotal Structures""; ""Doubles of (quasi) Hopf Algebras and Some Examples of Quantum Groupoids and Vertex Groups Related to Them""; ""Central Braided Hopf Algebras""; ""A Note on Anti-Yetter-Drinfeld Modules""; ""Representations of the Hopf Algebra U(n)""
Record Nr. UNINA-9910808662003321
Providence, Rhode Island : , : American Mathematical Society, , [2007]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Hopf algebras and tensor categories : international conference, July 4-8, 2011, University of Almería, Almería, Spain / / Nicolás Andruskiewitsch, Juan Cuadra, Blas Torrecillas, editors
Hopf algebras and tensor categories : international conference, July 4-8, 2011, University of Almería, Almería, Spain / / Nicolás Andruskiewitsch, Juan Cuadra, Blas Torrecillas, editors
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , 2013
Descrizione fisica 1 online resource (346 p.)
Disciplina 512/.46
Collana Contemporary Mathematics
Soggetto topico Hopf algebras
Soggetto genere / forma Electronic books.
ISBN 0-8218-9498-6
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""Preface""; ""Conference program""; ""Unified products and split extensions of Hopf algebras""; ""Introduction""; ""1. Preliminaries""; ""2. Unifying products versus split extensions of Hopf algebras""; ""References""; ""Hopf monoids in the category of species""; ""Introduction""; ""1. Preliminaries on compositions and partitions""; ""2. Species and Hopf monoids""; ""3. The Hadamard product""; ""4. Set species and set-theoretic Hopf monoids""; ""5. Connected Hopf monoids""; ""6. The free monoid""; ""7. The free commutative monoid""; ""8. The free Lie monoid""; ""9. Examples of Hopf monoids""
""On the double crossed product of weak Hopf algebras""""Introduction""; ""1. Double crossed product of weak bialgebras""; ""2. The antipode""; ""3. Examples""; ""Appendix A. Diagrams""; ""References""; ""The doubles of a braided Hopf algebra""; ""Introduction""; ""1. Preliminaries on categories""; ""2. Hopf algebras in braided categories""; ""3. Hopf monads""; ""4. The central double of a Hopf algebra""; ""5. Cross products and cross quotients of Hopf monads""; ""References""; ""Induced Conjugacy Classes and Induced _{ }( )-Modules""; ""1. Introduction""; ""2. Notation""; ""References""
""Recovering information from character tables of Hopf algebras: normality, dimensions and quotients""""introduction""; ""Preliminaries""; ""1. Retrieving information from the character table""; ""Acknowledgments""; ""References""; ""Hom-quasi-bialgebras""; ""1. Introduction""; ""2. Overview of Hom-associative algebras, Hom-coalgebras and Hom-bialgebras""; ""3. Hom-quasi-bialgebras (HQ-bialgebras)""; ""4. Gauge Transformation and Drinfeld�s Twist Construction for HQ-bialgebras""; ""5. Twisted quantum double, an example""; ""References""
""On twisted conjugacy classes of type D in sporadic simple groups""""1. Introduction""; ""2. Preliminaries""; ""3. Proof of Theorem 1.1""; ""4. Appendix: the sporadic simple groups""; ""References""; ""Partial and unified crossed products are weak crossed products""; ""Introduction""; ""1. The general theory of weak crossed products""; ""2. Partial crossed products are weak crossed products""; ""3. Unified products are weak crossed products""; ""References""; ""The Green rings of the generalized Taft Hopf algebras""; ""1. Introduction""
""2. Representation theory of the generalized Taft algebra _{ , }""
Record Nr. UNINA-9910481004003321
Providence, Rhode Island : , : American Mathematical Society, , 2013
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Hopf algebras and tensor categories : international conference, July 4-8, 2011, University of Almería, Almería, Spain / / Nicolás Andruskiewitsch, Juan Cuadra, Blas Torrecillas, editors
Hopf algebras and tensor categories : international conference, July 4-8, 2011, University of Almería, Almería, Spain / / Nicolás Andruskiewitsch, Juan Cuadra, Blas Torrecillas, editors
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , 2013
Descrizione fisica 1 online resource (346 p.)
Disciplina 512/.46
Collana Contemporary mathematics
Soggetto topico Hopf algebras
ISBN 0-8218-9498-6
Classificazione 16T0516T1016S4016T3017B3517B3718D1018C1519A22
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Preface -- Conference program -- Unified products and split extensions of Hopf algebras -- Introduction -- Hopf monoids in the category of species -- On the double crossed product of weak Hopf algebras -- The doubles of a braided Hopf algebra -- Induced Conjugacy Classes and Induced _{ }( )-Modules -- Recovering information from character tables of Hopf algebras: normality, dimensions and quotients -- Hom-quasi-bi-algebras -- On twisted conjugacy classes of type D in sporadic simple groups -- Partial and unified crossed products are weak crossed products -- The Green rings of the generalized Taft Hopf algebras -- Morita equivalence methods in classification of fusion categories.
Record Nr. UNINA-9910788766103321
Providence, Rhode Island : , : American Mathematical Society, , 2013
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Hopf algebras and tensor categories : international conference, July 4-8, 2011, University of Almería, Almería, Spain / / Nicolás Andruskiewitsch, Juan Cuadra, Blas Torrecillas, editors
Hopf algebras and tensor categories : international conference, July 4-8, 2011, University of Almería, Almería, Spain / / Nicolás Andruskiewitsch, Juan Cuadra, Blas Torrecillas, editors
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , 2013
Descrizione fisica 1 online resource (346 p.)
Disciplina 512/.46
Collana Contemporary mathematics
Soggetto topico Hopf algebras
ISBN 0-8218-9498-6
Classificazione 16T0516T1016S4016T3017B3517B3718D1018C1519A22
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Preface -- Conference program -- Unified products and split extensions of Hopf algebras -- Introduction -- Hopf monoids in the category of species -- On the double crossed product of weak Hopf algebras -- The doubles of a braided Hopf algebra -- Induced Conjugacy Classes and Induced _{ }( )-Modules -- Recovering information from character tables of Hopf algebras: normality, dimensions and quotients -- Hom-quasi-bi-algebras -- On twisted conjugacy classes of type D in sporadic simple groups -- Partial and unified crossed products are weak crossed products -- The Green rings of the generalized Taft Hopf algebras -- Morita equivalence methods in classification of fusion categories.
Record Nr. UNINA-9910818982003321
Providence, Rhode Island : , : American Mathematical Society, , 2013
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Hopf algebras and their generalizations from a category theoretical point of view [e-book] / Gabriella Böhm
Hopf algebras and their generalizations from a category theoretical point of view [e-book] / Gabriella Böhm
Autore Böhm, Gabriella
Descrizione fisica 1 online resource (xi, 165 pages) : illustrations
Disciplina 512.55
Collana Lecture notes in mathematics, 0075-8434 ; 2226
Soggetto topico Hopf algebras
ISBN 3319981374
9783319981376
9783319981369
Classificazione AMS 16T05
AMS 16T10
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISALENTO-991003635329707536
Böhm, Gabriella  
Materiale a stampa
Lo trovi qui: Univ. del Salento
Opac: Controlla la disponibilità qui