Semisolvability of semisimple Hopf algebras of low dimension / / Sonia Natale

• Record Nr.: UNINA9910819099303321
• Autore: Natale Sonia <1972->
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , 2007; ©2007
• ISBN: 1-4704-0478-8
• Descrizione fisica: 1 online resource (138 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; Volume 186, Number 874
• Classificazione: 31.23
• Disciplina: 512.55
• Soggetti: Hopf algebras; Quantum groups
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "Volume 186, Number 874 (fourth of five numbers)."
• Nota di bibliografia: Includes bibliographical references.
• 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""