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Rational homotopical models and uniqueness / / Martin Majewski
Rational homotopical models and uniqueness / / Martin Majewski
Autore Majewski Martin <1963->
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , [2000]
Descrizione fisica 1 online resource (175 p.)
Disciplina 510 s
514/.24
Collana Memoirs of the American Mathematical Society
Soggetto topico Homotopy theory
Hopf algebras
ISBN 1-4704-0273-4
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""TABLE OF CONTENTS""; ""ABSTRACT""; ""KEYWORDS""; ""PREFACE""; ""INTRODUCTION""; ""1. HOMOTOPY THEORY""; ""1. HOMOTOPICAL CATEGORIES""; ""1. The axioms""; ""2. Left homotopical categories""; ""3. Homotopical subcategories""; ""2. FUNDAMENTAL RESULTS""; ""1. Lifting and extension""; ""2. The derived category""; ""3. Homotopical functors and their derived functors""; ""4. The Adjoint Functor Theorem""; ""3. COMONOIDS UP TO HOMOTOPY""; ""1. � as comonoids over the derived category""; ""2. Derived tensor product""; ""3. Generalizations""; ""A. EXAMPLES OF HOMOTOPICAL CATEGORIES""
""1. Cofibration categories""""2. Model categories""; ""3. Spaces""; ""4. Simplicial objects""; ""2. DIFFERENTIAL ALGEBRA""; ""1. PRELIMINARIES""; ""1. Chain complexes""; ""2. DG (co)algebras""; ""3. Tensor (co) algebras""; ""2. TWISTING MAPS AND THE (CO) BAR CONSTRUCTION""; ""1. Twisting maps and homotopies""; ""2. The (co)bar construction""; ""3. Compatibility with tensor product""; ""4. Homological properties""; ""3. ACYCLIC MODELS""; ""1. Representable functors""; ""2. The method of acyclic models""; ""3. Duality""; ""4. Acyclic model theorems for twisting maps""; ""4. EZ-MORPHISMS""
""1. Extension of an EZ-morphism""""2. A generalization""; ""3. Properties of the extension""; ""B. CHAIN (CO) FUNCTORS""; ""1. Monoidal categories""; ""2. Normalization""; ""3. Representable cofunctors for spaces""; ""4. Cohomology theories""; ""3. COMPLETE ALGEBRA""; ""1. COMPLETE AUGMENTED ALGEBRAS""; ""1. Ring systems""; ""2. Complete modules""; ""3. Complete augmented algebras and free groups""; ""4. Rigidity""; ""2. COMPLETE LIE ALGEBRAS AND COMPLETE HOPF ALGEBRAS""; ""1. Complete Hopf algebras and the exponential mapping""; ""2. The PBW�Theorem""; ""3. Normal complete Hopf algebras""
""4. Rigidity""""3. COMPLETE GROUPS""; ""1. Nilpotent groups""; ""2. Complete groups""; ""3. The Lazard � Mal'cev correspondence""; ""4. The Quillen functor""; ""C. FILTERED MODULES""; ""1. Filtered vs. cofiltered modules""; ""2. Normal maps and exactness""; ""3. Filtered tensor product""; ""4. Complete Differential Algebra""; ""4. THREE MODELS FOR SPACES""; ""1. THE CELLULAR MODEL""; ""1. The homotopical category of dg algebras""; ""2. The homotopical category of dg Hopf algebras up to homotopy""; ""3. The cobar � chain functor and the chain � loop functor""
""4. Compatibility with (tensor) products""""5. The homotopy diagonals""; ""2. THE SULLIVAN MODEL""; ""1. The homotopical category of commutative dg* algebras""; ""2. The Sullivan cofunctor and Stokes' map""; ""3. Extension of Stokes' map""; ""4. Compatibility with (tensor) products""; ""5. Dualization""; ""6. The homotopy diagonals""; ""3. THE QUILLEN MODEL""; ""1. The homotopical category of dg Lie algebras""; ""2. The Quillen functor""; ""3. Connection to the chain � loop functor""; ""4. The group algebra of a free simplicial group""; ""5. A proof of the Quillen equivalence""
""4. MAIN RESULTS""
Record Nr. UNINA-9910788739503321
Majewski Martin <1963->  
Providence, Rhode Island : , : American Mathematical Society, , [2000]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Rational homotopical models and uniqueness / / Martin Majewski
Rational homotopical models and uniqueness / / Martin Majewski
Autore Majewski Martin <1963->
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , [2000]
Descrizione fisica 1 online resource (175 p.)
Disciplina 510 s
514/.24
Collana Memoirs of the American Mathematical Society
Soggetto topico Homotopy theory
Hopf algebras
ISBN 1-4704-0273-4
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""TABLE OF CONTENTS""; ""ABSTRACT""; ""KEYWORDS""; ""PREFACE""; ""INTRODUCTION""; ""1. HOMOTOPY THEORY""; ""1. HOMOTOPICAL CATEGORIES""; ""1. The axioms""; ""2. Left homotopical categories""; ""3. Homotopical subcategories""; ""2. FUNDAMENTAL RESULTS""; ""1. Lifting and extension""; ""2. The derived category""; ""3. Homotopical functors and their derived functors""; ""4. The Adjoint Functor Theorem""; ""3. COMONOIDS UP TO HOMOTOPY""; ""1. � as comonoids over the derived category""; ""2. Derived tensor product""; ""3. Generalizations""; ""A. EXAMPLES OF HOMOTOPICAL CATEGORIES""
""1. Cofibration categories""""2. Model categories""; ""3. Spaces""; ""4. Simplicial objects""; ""2. DIFFERENTIAL ALGEBRA""; ""1. PRELIMINARIES""; ""1. Chain complexes""; ""2. DG (co)algebras""; ""3. Tensor (co) algebras""; ""2. TWISTING MAPS AND THE (CO) BAR CONSTRUCTION""; ""1. Twisting maps and homotopies""; ""2. The (co)bar construction""; ""3. Compatibility with tensor product""; ""4. Homological properties""; ""3. ACYCLIC MODELS""; ""1. Representable functors""; ""2. The method of acyclic models""; ""3. Duality""; ""4. Acyclic model theorems for twisting maps""; ""4. EZ-MORPHISMS""
""1. Extension of an EZ-morphism""""2. A generalization""; ""3. Properties of the extension""; ""B. CHAIN (CO) FUNCTORS""; ""1. Monoidal categories""; ""2. Normalization""; ""3. Representable cofunctors for spaces""; ""4. Cohomology theories""; ""3. COMPLETE ALGEBRA""; ""1. COMPLETE AUGMENTED ALGEBRAS""; ""1. Ring systems""; ""2. Complete modules""; ""3. Complete augmented algebras and free groups""; ""4. Rigidity""; ""2. COMPLETE LIE ALGEBRAS AND COMPLETE HOPF ALGEBRAS""; ""1. Complete Hopf algebras and the exponential mapping""; ""2. The PBW�Theorem""; ""3. Normal complete Hopf algebras""
""4. Rigidity""""3. COMPLETE GROUPS""; ""1. Nilpotent groups""; ""2. Complete groups""; ""3. The Lazard � Mal'cev correspondence""; ""4. The Quillen functor""; ""C. FILTERED MODULES""; ""1. Filtered vs. cofiltered modules""; ""2. Normal maps and exactness""; ""3. Filtered tensor product""; ""4. Complete Differential Algebra""; ""4. THREE MODELS FOR SPACES""; ""1. THE CELLULAR MODEL""; ""1. The homotopical category of dg algebras""; ""2. The homotopical category of dg Hopf algebras up to homotopy""; ""3. The cobar � chain functor and the chain � loop functor""
""4. Compatibility with (tensor) products""""5. The homotopy diagonals""; ""2. THE SULLIVAN MODEL""; ""1. The homotopical category of commutative dg* algebras""; ""2. The Sullivan cofunctor and Stokes' map""; ""3. Extension of Stokes' map""; ""4. Compatibility with (tensor) products""; ""5. Dualization""; ""6. The homotopy diagonals""; ""3. THE QUILLEN MODEL""; ""1. The homotopical category of dg Lie algebras""; ""2. The Quillen functor""; ""3. Connection to the chain � loop functor""; ""4. The group algebra of a free simplicial group""; ""5. A proof of the Quillen equivalence""
""4. MAIN RESULTS""
Record Nr. UNINA-9910812747003321
Majewski Martin <1963->  
Providence, Rhode Island : , : American Mathematical Society, , [2000]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Representations of finite classical groups : a Hopf algebra approach / Andrey V. Zelevinsky
Representations of finite classical groups : a Hopf algebra approach / Andrey V. Zelevinsky
Autore Zelevinsky, Andrey V.
Pubbl/distr/stampa Berlin ; New York : Springer-Verlag, 1981
Descrizione fisica iv, 184 p. ; 24 cm.
Disciplina 510
Collana Lecture notes in mathematics, 0075-8434 ; 869
Soggetto topico Finite groups
Hopf algebras
Representations of groups
ISBN 0540108246
Classificazione AMS 20C30
AMS 20G05
AMS 20G40
QA3
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISALENTO-991001300329707536
Zelevinsky, Andrey V.  
Berlin ; New York : Springer-Verlag, 1981
Materiale a stampa
Lo trovi qui: Univ. del Salento
Opac: Controlla la disponibilità qui
Semisolvability of semisimple Hopf algebras of low dimension / / Sonia Natale
Semisolvability of semisimple Hopf algebras of low dimension / / Sonia Natale
Autore Natale Sonia <1972->
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , 2007
Descrizione fisica 1 online resource (138 p.)
Disciplina 512.55
Collana Memoirs of the American Mathematical Society
Soggetto topico Hopf algebras
Quantum groups
Soggetto genere / forma Electronic books.
ISBN 1-4704-0478-8
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""Contents""; ""Introduction and Main Results""; ""Conventions and Notation""; ""Chapter 1. Semisimple Hopf Algebras""; ""1.1. Algebra structure""; ""1.2. Irreducible characters""; ""1.3. Coinvariants of Hopf algebra maps""; ""1.4. Yetter- Drinfeld modules""; ""1.5. Yetter- Drinfeld modules and the character algebra""; ""1.6. One dimensional Yetter- Drinfeld modules""; ""1.7. H[sup(coB)] as a left coideal of H""; ""Chapter 2. The Nichols-Richmond Theorem""; ""2.1. Irreducible characters of degree 2""; ""2.2. The Nichols-Richmond theorem""; ""2.3. An application to D(H)""
""2.4. Existence of proper Hopf subalgebras""""2.5. Hopf subalgebras of index 3""; ""Chapter 3. Quotient Coalgebras""; ""3.1. A multiplicity formula""; ""3.2. Stable subcoalgebras""; ""3.3. Quotients modulo group- like Hopf subalgebras""; ""3.4. On the structure of G(H)""; ""3.5. A criterion of normality""; ""Chapter 4. Braided Hopf Algebras""; ""4.1. Radford- Majid biproduct construction""; ""4.2. Coalgebra structure of R""; ""4.3. Hopf subalgebras""; ""4.4. Biproducts over finite groups""; ""4.5. Cocommutative braided Hopf algebras""
""4.6. Cocommutative braided Hopf algebras over Z[sub(p)]""""4.7. Transitive actions of central subgroups""; ""Chapter 5. Cocycle Deformations of Some Hopf Algebras""; ""5.1. Lifting from abelian groups""; ""5.2. Examples in dimension pq[sup(2)]; p = 1 mod q""; ""5.3. Examples in dimension pq[sup(2)]; q = 1 mod p""; ""5.4. Normal Hopf subalgebras in cocycle twists""; ""Chapter 6. Dimension 24""; ""6.1. Possible (co)-algebra structures""; ""6.2. Upper and lower semisolvability""; ""Chapter 7. Dimension 30""; ""7.1. Possible (co)-algebra structures""; ""7.2. Classification""
""Chapter 8. Dimension 36""""8.1. Reduction of the problem""; ""8.2. Main result""; ""Chapter 9. Dimension 40""; ""9.1. Reduction of the problem""; ""9.2. Main result""; ""Chapter 10. Dimension 42""; ""10.1. Possible (co)-algebra structures""; ""10.2. Classification""; ""Chapter 11. Dimension 48""; ""11.1. First reduction""; ""11.2. Further reductions""; ""11.3. Main result up to cocycle twists""; ""11.4. Main result""; ""Chapter 12. Dimension 54""; ""12.1. First reduction""; ""12.2. Main result""; ""Chapter 13. Dimension 56""; ""13.1. First reduction""; ""13.2. Main result""
""Appendix A. Drinfeld Double of H[sub(8)]""""A.1. Structure of D(H[sub(8)])""; ""A.2. Proof of Theorem A.1.1""; ""A.3. Proof of Theorem A.1.2""; ""Bibliography""
Record Nr. UNINA-9910480978703321
Natale Sonia <1972->  
Providence, Rhode Island : , : American Mathematical Society, , 2007
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Semisolvability of semisimple Hopf algebras of low dimension / / Sonia Natale
Semisolvability of semisimple Hopf algebras of low dimension / / Sonia Natale
Autore Natale Sonia <1972->
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , 2007
Descrizione fisica 1 online resource (138 p.)
Disciplina 512.55
Collana Memoirs of the American Mathematical Society
Soggetto topico Hopf algebras
Quantum groups
ISBN 1-4704-0478-8
Classificazione 31.23
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""Contents""; ""Introduction and Main Results""; ""Conventions and Notation""; ""Chapter 1. Semisimple Hopf Algebras""; ""1.1. Algebra structure""; ""1.2. Irreducible characters""; ""1.3. Coinvariants of Hopf algebra maps""; ""1.4. Yetter- Drinfeld modules""; ""1.5. Yetter- Drinfeld modules and the character algebra""; ""1.6. One dimensional Yetter- Drinfeld modules""; ""1.7. H[sup(coB)] as a left coideal of H""; ""Chapter 2. The Nichols-Richmond Theorem""; ""2.1. Irreducible characters of degree 2""; ""2.2. The Nichols-Richmond theorem""; ""2.3. An application to D(H)""
""2.4. Existence of proper Hopf subalgebras""""2.5. Hopf subalgebras of index 3""; ""Chapter 3. Quotient Coalgebras""; ""3.1. A multiplicity formula""; ""3.2. Stable subcoalgebras""; ""3.3. Quotients modulo group- like Hopf subalgebras""; ""3.4. On the structure of G(H)""; ""3.5. A criterion of normality""; ""Chapter 4. Braided Hopf Algebras""; ""4.1. Radford- Majid biproduct construction""; ""4.2. Coalgebra structure of R""; ""4.3. Hopf subalgebras""; ""4.4. Biproducts over finite groups""; ""4.5. Cocommutative braided Hopf algebras""
""4.6. Cocommutative braided Hopf algebras over Z[sub(p)]""""4.7. Transitive actions of central subgroups""; ""Chapter 5. Cocycle Deformations of Some Hopf Algebras""; ""5.1. Lifting from abelian groups""; ""5.2. Examples in dimension pq[sup(2)]; p = 1 mod q""; ""5.3. Examples in dimension pq[sup(2)]; q = 1 mod p""; ""5.4. Normal Hopf subalgebras in cocycle twists""; ""Chapter 6. Dimension 24""; ""6.1. Possible (co)-algebra structures""; ""6.2. Upper and lower semisolvability""; ""Chapter 7. Dimension 30""; ""7.1. Possible (co)-algebra structures""; ""7.2. Classification""
""Chapter 8. Dimension 36""""8.1. Reduction of the problem""; ""8.2. Main result""; ""Chapter 9. Dimension 40""; ""9.1. Reduction of the problem""; ""9.2. Main result""; ""Chapter 10. Dimension 42""; ""10.1. Possible (co)-algebra structures""; ""10.2. Classification""; ""Chapter 11. Dimension 48""; ""11.1. First reduction""; ""11.2. Further reductions""; ""11.3. Main result up to cocycle twists""; ""11.4. Main result""; ""Chapter 12. Dimension 54""; ""12.1. First reduction""; ""12.2. Main result""; ""Chapter 13. Dimension 56""; ""13.1. First reduction""; ""13.2. Main result""
""Appendix A. Drinfeld Double of H[sub(8)]""""A.1. Structure of D(H[sub(8)])""; ""A.2. Proof of Theorem A.1.1""; ""A.3. Proof of Theorem A.1.2""; ""Bibliography""
Record Nr. UNINA-9910788743703321
Natale Sonia <1972->  
Providence, Rhode Island : , : American Mathematical Society, , 2007
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Semisolvability of semisimple Hopf algebras of low dimension / / Sonia Natale
Semisolvability of semisimple Hopf algebras of low dimension / / Sonia Natale
Autore Natale Sonia <1972->
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , 2007
Descrizione fisica 1 online resource (138 p.)
Disciplina 512.55
Collana Memoirs of the American Mathematical Society
Soggetto topico Hopf algebras
Quantum groups
ISBN 1-4704-0478-8
Classificazione 31.23
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""Contents""; ""Introduction and Main Results""; ""Conventions and Notation""; ""Chapter 1. Semisimple Hopf Algebras""; ""1.1. Algebra structure""; ""1.2. Irreducible characters""; ""1.3. Coinvariants of Hopf algebra maps""; ""1.4. Yetter- Drinfeld modules""; ""1.5. Yetter- Drinfeld modules and the character algebra""; ""1.6. One dimensional Yetter- Drinfeld modules""; ""1.7. H[sup(coB)] as a left coideal of H""; ""Chapter 2. The Nichols-Richmond Theorem""; ""2.1. Irreducible characters of degree 2""; ""2.2. The Nichols-Richmond theorem""; ""2.3. An application to D(H)""
""2.4. Existence of proper Hopf subalgebras""""2.5. Hopf subalgebras of index 3""; ""Chapter 3. Quotient Coalgebras""; ""3.1. A multiplicity formula""; ""3.2. Stable subcoalgebras""; ""3.3. Quotients modulo group- like Hopf subalgebras""; ""3.4. On the structure of G(H)""; ""3.5. A criterion of normality""; ""Chapter 4. Braided Hopf Algebras""; ""4.1. Radford- Majid biproduct construction""; ""4.2. Coalgebra structure of R""; ""4.3. Hopf subalgebras""; ""4.4. Biproducts over finite groups""; ""4.5. Cocommutative braided Hopf algebras""
""4.6. Cocommutative braided Hopf algebras over Z[sub(p)]""""4.7. Transitive actions of central subgroups""; ""Chapter 5. Cocycle Deformations of Some Hopf Algebras""; ""5.1. Lifting from abelian groups""; ""5.2. Examples in dimension pq[sup(2)]; p = 1 mod q""; ""5.3. Examples in dimension pq[sup(2)]; q = 1 mod p""; ""5.4. Normal Hopf subalgebras in cocycle twists""; ""Chapter 6. Dimension 24""; ""6.1. Possible (co)-algebra structures""; ""6.2. Upper and lower semisolvability""; ""Chapter 7. Dimension 30""; ""7.1. Possible (co)-algebra structures""; ""7.2. Classification""
""Chapter 8. Dimension 36""""8.1. Reduction of the problem""; ""8.2. Main result""; ""Chapter 9. Dimension 40""; ""9.1. Reduction of the problem""; ""9.2. Main result""; ""Chapter 10. Dimension 42""; ""10.1. Possible (co)-algebra structures""; ""10.2. Classification""; ""Chapter 11. Dimension 48""; ""11.1. First reduction""; ""11.2. Further reductions""; ""11.3. Main result up to cocycle twists""; ""11.4. Main result""; ""Chapter 12. Dimension 54""; ""12.1. First reduction""; ""12.2. Main result""; ""Chapter 13. Dimension 56""; ""13.1. First reduction""; ""13.2. Main result""
""Appendix A. Drinfeld Double of H[sub(8)]""""A.1. Structure of D(H[sub(8)])""; ""A.2. Proof of Theorem A.1.1""; ""A.3. Proof of Theorem A.1.2""; ""Bibliography""
Record Nr. UNINA-9910819099303321
Natale Sonia <1972->  
Providence, Rhode Island : , : American Mathematical Society, , 2007
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Spectral sequence constructors in algebra and topology / / D.W. Barnes
Spectral sequence constructors in algebra and topology / / D.W. Barnes
Autore Barnes D. W (Donald W.), <1935->
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , 1985
Descrizione fisica 1 online resource (187 p.)
Disciplina 512/.55
Collana Memoirs of the American Mathematical Society
Soggetto topico Functor theory
Spectral sequences (Mathematics)
Hopf algebras
Soggetto genere / forma Electronic books.
ISBN 1-4704-0730-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""CONTENTS""; ""PREFACE""; ""I. MODULES OVER HOPE ALGEBRAS""; ""1. Hopf Algebras""; ""2. Groups""; ""3. Lie Algebras""; ""4. Modules""; ""5. Homology and Cohomology""; ""II. CUP PRODUCTS""; ""1. Introduction""; ""2. Relatively Injective Modules""; ""3. Relatively Injective Resolutions""; ""4. General Resolutions""; ""III. SPECTRAL SEQUENCE CONSTRUCTORS""; ""1. Introduction""; ""2. Comparison of Spectral Sequence Constructors""; ""3. Cup Products""; ""IV. FILTRATIONS ON THE NORMALISED STANDARD COMPLEX""; ""1. Introduction""; ""2. Comparison of the Filtrations""
""3. Calculation of the E[sub(1)]â€?term""""4. Lie Algebras""; ""5. The Adams Spectral Sequence""; ""V. DOUBLE PROJECTIVE RESOLUTIONS""; ""1. The Construction""; ""2. Calculation of the E[sub(1)]â€?term""; ""3. Cup Products""; ""VI. PAIR OF RESOLUTIONS""; ""1. Introduction""; ""2. The Coinduced Resolution""; ""3. Cup Products""; ""VII. REPEATED INJECTIVE RESOLUTIONS""; ""1. The Grothendieck Construction""; ""2. Repeated Coinduced Resolutions""; ""VIII. EXPLICIT EQUIVALENCES""; ""1. Survey of Spectral Sequence Constructors""; ""2. Transformation B â?? A*""; ""3. Transformation C â?? A*""
""4. Transformation B â?? C""""IX. ACYCLIC MODELS""; ""1. Free Functors""; ""2. Chain Complexes""; ""3 . Filtered Chain Complexes""; ""4. The Uniqueness Theorem""; ""X. COFREE FUNCTORS""; ""1. Free Functors Reformulated""; ""2. Cofree Functors""; ""3. Right Derived Functors""; ""4. Filtered Cochain Complexes""; ""5. The Uniqueness Theorem""; ""XI. LOCAL COEFFICIENTS""; ""1. Homology with Local Coefficients""; ""2. The Uniqueness Theorem""; ""3. Homomorphisms""; ""XII. THE SPECTRAL SEQUENCE OF A FIBRATION""; ""1. Introduction""; ""2. The Classifying Space of a Group""; ""3. Fibrations""
""4. Calculation of the E[sup(2)]�term""""5. Other Constructions""; ""XIII. UNIQUENESS OF THE FIBRATION SPECTRAL SEQUENCE""; ""1. The Fibration Spectral Sequence Constructor Axioms""; ""2. The E[sup(1)][sub(*0)] Axiom""; ""3. The Comparison Theorem""; ""4. The uniqueness Theorem""; ""XIV. SHEAF COHOMOLOGY""; ""1. Sheaves""; ""2. Change of Base""; ""3. Sheaf Cohomology""; ""4. Locally Constant Sheaves""; ""5. The Leray Spectral Sequence""; ""APPENDIX. LIFTING FUNCTIONS""; ""REFERENCES""; ""INDEX""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""K""; ""L""; ""M""; ""N""
""P""""Q""; ""R""; ""S""; ""T""; ""U""; ""V""
Record Nr. UNINA-9910480477603321
Barnes D. W (Donald W.), <1935->  
Providence, Rhode Island : , : American Mathematical Society, , 1985
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Spectral sequence constructors in algebra and topology / / D.W. Barnes
Spectral sequence constructors in algebra and topology / / D.W. Barnes
Autore Barnes D. W (Donald W.), <1935->
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , 1985
Descrizione fisica 1 online resource (187 p.)
Disciplina 512/.55
Collana Memoirs of the American Mathematical Society
Soggetto topico Functor theory
Spectral sequences (Mathematics)
Hopf algebras
ISBN 1-4704-0730-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""CONTENTS""; ""PREFACE""; ""I. MODULES OVER HOPE ALGEBRAS""; ""1. Hopf Algebras""; ""2. Groups""; ""3. Lie Algebras""; ""4. Modules""; ""5. Homology and Cohomology""; ""II. CUP PRODUCTS""; ""1. Introduction""; ""2. Relatively Injective Modules""; ""3. Relatively Injective Resolutions""; ""4. General Resolutions""; ""III. SPECTRAL SEQUENCE CONSTRUCTORS""; ""1. Introduction""; ""2. Comparison of Spectral Sequence Constructors""; ""3. Cup Products""; ""IV. FILTRATIONS ON THE NORMALISED STANDARD COMPLEX""; ""1. Introduction""; ""2. Comparison of the Filtrations""
""3. Calculation of the E[sub(1)]â€?term""""4. Lie Algebras""; ""5. The Adams Spectral Sequence""; ""V. DOUBLE PROJECTIVE RESOLUTIONS""; ""1. The Construction""; ""2. Calculation of the E[sub(1)]â€?term""; ""3. Cup Products""; ""VI. PAIR OF RESOLUTIONS""; ""1. Introduction""; ""2. The Coinduced Resolution""; ""3. Cup Products""; ""VII. REPEATED INJECTIVE RESOLUTIONS""; ""1. The Grothendieck Construction""; ""2. Repeated Coinduced Resolutions""; ""VIII. EXPLICIT EQUIVALENCES""; ""1. Survey of Spectral Sequence Constructors""; ""2. Transformation B â?? A*""; ""3. Transformation C â?? A*""
""4. Transformation B â?? C""""IX. ACYCLIC MODELS""; ""1. Free Functors""; ""2. Chain Complexes""; ""3 . Filtered Chain Complexes""; ""4. The Uniqueness Theorem""; ""X. COFREE FUNCTORS""; ""1. Free Functors Reformulated""; ""2. Cofree Functors""; ""3. Right Derived Functors""; ""4. Filtered Cochain Complexes""; ""5. The Uniqueness Theorem""; ""XI. LOCAL COEFFICIENTS""; ""1. Homology with Local Coefficients""; ""2. The Uniqueness Theorem""; ""3. Homomorphisms""; ""XII. THE SPECTRAL SEQUENCE OF A FIBRATION""; ""1. Introduction""; ""2. The Classifying Space of a Group""; ""3. Fibrations""
""4. Calculation of the E[sup(2)]�term""""5. Other Constructions""; ""XIII. UNIQUENESS OF THE FIBRATION SPECTRAL SEQUENCE""; ""1. The Fibration Spectral Sequence Constructor Axioms""; ""2. The E[sup(1)][sub(*0)] Axiom""; ""3. The Comparison Theorem""; ""4. The uniqueness Theorem""; ""XIV. SHEAF COHOMOLOGY""; ""1. Sheaves""; ""2. Change of Base""; ""3. Sheaf Cohomology""; ""4. Locally Constant Sheaves""; ""5. The Leray Spectral Sequence""; ""APPENDIX. LIFTING FUNCTIONS""; ""REFERENCES""; ""INDEX""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""K""; ""L""; ""M""; ""N""
""P""""Q""; ""R""; ""S""; ""T""; ""U""; ""V""
Record Nr. UNINA-9910788890103321
Barnes D. W (Donald W.), <1935->  
Providence, Rhode Island : , : American Mathematical Society, , 1985
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Spectral sequence constructors in algebra and topology / / D.W. Barnes
Spectral sequence constructors in algebra and topology / / D.W. Barnes
Autore Barnes D. W (Donald W.), <1935->
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , 1985
Descrizione fisica 1 online resource (187 p.)
Disciplina 512/.55
Collana Memoirs of the American Mathematical Society
Soggetto topico Functor theory
Spectral sequences (Mathematics)
Hopf algebras
ISBN 1-4704-0730-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""CONTENTS""; ""PREFACE""; ""I. MODULES OVER HOPE ALGEBRAS""; ""1. Hopf Algebras""; ""2. Groups""; ""3. Lie Algebras""; ""4. Modules""; ""5. Homology and Cohomology""; ""II. CUP PRODUCTS""; ""1. Introduction""; ""2. Relatively Injective Modules""; ""3. Relatively Injective Resolutions""; ""4. General Resolutions""; ""III. SPECTRAL SEQUENCE CONSTRUCTORS""; ""1. Introduction""; ""2. Comparison of Spectral Sequence Constructors""; ""3. Cup Products""; ""IV. FILTRATIONS ON THE NORMALISED STANDARD COMPLEX""; ""1. Introduction""; ""2. Comparison of the Filtrations""
""3. Calculation of the E[sub(1)]â€?term""""4. Lie Algebras""; ""5. The Adams Spectral Sequence""; ""V. DOUBLE PROJECTIVE RESOLUTIONS""; ""1. The Construction""; ""2. Calculation of the E[sub(1)]â€?term""; ""3. Cup Products""; ""VI. PAIR OF RESOLUTIONS""; ""1. Introduction""; ""2. The Coinduced Resolution""; ""3. Cup Products""; ""VII. REPEATED INJECTIVE RESOLUTIONS""; ""1. The Grothendieck Construction""; ""2. Repeated Coinduced Resolutions""; ""VIII. EXPLICIT EQUIVALENCES""; ""1. Survey of Spectral Sequence Constructors""; ""2. Transformation B â?? A*""; ""3. Transformation C â?? A*""
""4. Transformation B â?? C""""IX. ACYCLIC MODELS""; ""1. Free Functors""; ""2. Chain Complexes""; ""3 . Filtered Chain Complexes""; ""4. The Uniqueness Theorem""; ""X. COFREE FUNCTORS""; ""1. Free Functors Reformulated""; ""2. Cofree Functors""; ""3. Right Derived Functors""; ""4. Filtered Cochain Complexes""; ""5. The Uniqueness Theorem""; ""XI. LOCAL COEFFICIENTS""; ""1. Homology with Local Coefficients""; ""2. The Uniqueness Theorem""; ""3. Homomorphisms""; ""XII. THE SPECTRAL SEQUENCE OF A FIBRATION""; ""1. Introduction""; ""2. The Classifying Space of a Group""; ""3. Fibrations""
""4. Calculation of the E[sup(2)]�term""""5. Other Constructions""; ""XIII. UNIQUENESS OF THE FIBRATION SPECTRAL SEQUENCE""; ""1. The Fibration Spectral Sequence Constructor Axioms""; ""2. The E[sup(1)][sub(*0)] Axiom""; ""3. The Comparison Theorem""; ""4. The uniqueness Theorem""; ""XIV. SHEAF COHOMOLOGY""; ""1. Sheaves""; ""2. Change of Base""; ""3. Sheaf Cohomology""; ""4. Locally Constant Sheaves""; ""5. The Leray Spectral Sequence""; ""APPENDIX. LIFTING FUNCTIONS""; ""REFERENCES""; ""INDEX""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""K""; ""L""; ""M""; ""N""
""P""""Q""; ""R""; ""S""; ""T""; ""U""; ""V""
Record Nr. UNINA-9910828764203321
Barnes D. W (Donald W.), <1935->  
Providence, Rhode Island : , : American Mathematical Society, , 1985
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Squared Hopf algebras / / Volodymyr V. Lyubashenko
Squared Hopf algebras / / Volodymyr V. Lyubashenko
Autore Lyubashenko Volodymyr V. <1959->
Pubbl/distr/stampa Providence, Rhode Island : , : American Mathematical Society, , [1999]
Descrizione fisica 1 online resource (197 p.)
Disciplina 512/.55
Collana Memoirs of the American Mathematical Society
Soggetto topico Hopf algebras
Soggetto genere / forma Electronic books.
ISBN 1-4704-0268-8
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""Contents""; ""Introduction""; ""Chapter 1. Tools""; ""1.1. Tensor product of abelian categories""; ""1.2. Monoidal categories""; ""1.3. Monoidal abelian categories""; ""1.4. Symmetric monoidal 2-category of abelian categories""; ""1.5. System of notations""; ""1.6. Monoidal structures on V [omitted] V""; ""1.7. Ind-objects""; ""1.8. Rigid-abelian categories""; ""Chapter 2. Squared coalgebras""; ""2.1. Definitions""; ""2.2. Comodules""; ""2.3. The fundamental theorem on coalgebras""; ""2.4. Relationship between categories of comodules""; ""2.5. The category of fibre functors""
""2.6. Reconstruction theorems""""2.7. Comodules over ordinary coalgebras""; ""2.8. Construction data""; ""Chapter 3. Squared bicoalgebras""; ""3.1. Tensor product of squared coalgebras""; ""3.2. Bicoalgebras""; ""3.3. Monoidal construction data""; ""3.4. Tensor generators and relations""; ""3.5. Relationship with braided bialgebras""; ""3.6. Commutative algebras and braiding""; ""Chapter 4. Hopf coalgebras""; ""4.1. Opposite coalgebras""; ""4.2. Comparison with opposite coalgebra in braided case""; ""4.3. The antipode""; ""4.4. Comparison with braided Hopf algebras""
""4.5. Multiplication in the opposite bialgebra""""4.6. Reconstruction of rigid monoidal categories""; ""Chapter 5. Quasitriangular Hopf coalgebras""; ""5.1. R-matrices in Hopf coalgebras""; ""5.2. Braiding for comodules over a braided Hopf algebra""; ""5.3. Constructing braided categories""; ""5.4. Ribbon Hopf coalgebras""; ""5.5. Ribbon reconstruction""; ""Appendix A. Symmetric monoidal 2-categories""; ""A.1. A review of 2-categories""; ""A.2. 2-pasting schemes""; ""A.3. Weak 2-pasting""; ""A.4. Weak 3-categories""; ""A.5. A monoidal 2-category of abelian categories""
""A.6. Symmetric monoidal 2-categories""""A.7. A symmetric monoidal 2-category of abelian categories""; ""Bibliography""
Record Nr. UNINA-9910479924703321
Lyubashenko Volodymyr V. <1959->  
Providence, Rhode Island : , : American Mathematical Society, , [1999]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui