LEADER 04207nam 2200589 450 001 9910480978703321 005 20170822144408.0 010 $a1-4704-0478-8 035 $a(CKB)3360000000465058 035 $a(EBL)3114105 035 $a(SSID)ssj0000889206 035 $a(PQKBManifestationID)11478758 035 $a(PQKBTitleCode)TC0000889206 035 $a(PQKBWorkID)10876200 035 $a(PQKB)11270759 035 $a(MiAaPQ)EBC3114105 035 $a(PPN)195417631 035 $a(EXLCZ)993360000000465058 100 $a20150417h20072007 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSemisolvability of semisimple Hopf algebras of low dimension /$fSonia Natale 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2007. 210 4$dİ2007 215 $a1 online resource (138 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vVolume 186, Number 874 300 $a"Volume 186, Number 874 (fourth of five numbers)." 311 $a0-8218-3948-9 320 $aIncludes bibliographical references. 327 $a""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)"" 327 $a""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"" 327 $a""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"" 327 $a""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"" 327 $a""Appendix A. Drinfeld Double of H[sub(8)]""""A.1. Structure of D(H[sub(8)])""; ""A.2. Proof of Theorem A.1.1""; ""A.3. Proof of Theorem A.1.2""; ""Bibliography"" 410 0$aMemoirs of the American Mathematical Society ;$vVolume 186, Number 874. 606 $aHopf algebras 606 $aQuantum groups 608 $aElectronic books. 615 0$aHopf algebras. 615 0$aQuantum groups. 676 $a512.55 700 $aNatale$b Sonia$f1972-$0940172 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910480978703321 996 $aSemisolvability of semisimple Hopf algebras of low dimension$92119987 997 $aUNINA