04207nam 2200589 450 991048097870332120170822144408.01-4704-0478-8(CKB)3360000000465058(EBL)3114105(SSID)ssj0000889206(PQKBManifestationID)11478758(PQKBTitleCode)TC0000889206(PQKBWorkID)10876200(PQKB)11270759(MiAaPQ)EBC3114105(PPN)195417631(EXLCZ)99336000000046505820150417h20072007 uy 0engur|n|---|||||txtccrSemisolvability of semisimple Hopf algebras of low dimension /Sonia NataleProvidence, Rhode Island :American Mathematical Society,2007.©20071 online resource (138 p.)Memoirs of the American Mathematical Society,0065-9266 ;Volume 186, Number 874"Volume 186, Number 874 (fourth of five numbers)."0-8218-3948-9 Includes bibliographical references.""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""Memoirs of the American Mathematical Society ;Volume 186, Number 874.Hopf algebrasQuantum groupsElectronic books.Hopf algebras.Quantum groups.512.55Natale Sonia1972-940172MiAaPQMiAaPQMiAaPQBOOK9910480978703321Semisolvability of semisimple Hopf algebras of low dimension2119987UNINA