LEADER 03664nam 2200649 450 001 9910479856303321 005 20170822144306.0 010 $a1-4704-0459-1 035 $a(CKB)3360000000465039 035 $a(EBL)3114251 035 $a(SSID)ssj0000889108 035 $a(PQKBManifestationID)11523069 035 $a(PQKBTitleCode)TC0000889108 035 $a(PQKBWorkID)10875533 035 $a(PQKB)11642747 035 $a(MiAaPQ)EBC3114251 035 $a(PPN)195417437 035 $a(EXLCZ)993360000000465039 100 $a20060111h20062006 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aOn higher Frobenius-Schur indicators /$fYevgenia Kashina, Yorck Sommerha?user, Yongchang Zhu 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[2006] 210 4$dİ2006 215 $a1 online resource (82 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vnumber 855 300 $a"Volume 181, number 855 (fourth of 5 numbers)." 311 $a0-8218-3886-5 320 $aIncludes bibliographical references (pages 59-60) and indexes. 327 $a""Contents""; ""Introduction""; ""Chapter 1. The Calculus of Sweedler Powers""; ""1.1. Monotone maps""; ""1.2. The union of the symmetric groups""; ""1.3. Bialgebras""; ""1.4. A monoid""; ""1.5. Permutations from sequences""; ""1.6. Sweedler powers""; ""Chapter 2. Frobenius-Schur Indicators""; ""2.1. Central Sweedler powers""; ""2.2. The coproduct of the Sweedler powers""; ""2.3. The first formula for the Frobenius-Schur indicators""; ""2.4. The Frobenius-Schur theorem""; ""2.5. Frobenius-Schur indicators of the regular representation""; ""Chapter 3. The Exponent""; ""3.1. The exponent"" 327 $a""3.2. The second formula for the Frobenius-Schur indicators""""3.3. Sweedler powers of the integral""; ""3.4. Cauchy's theorem""; ""Chapter 4. The Order""; ""4.1. Order and multiplicity""; ""4.2. The divisibility theorem""; ""4.3. An example""; ""4.4. The dimension of the simple modules""; ""Chapter 5. The Index""; ""5.1. Indecomposable matrices""; ""5.2. The normal form""; ""5.3. The Perron-Frobenius theorem""; ""5.4. The index formula""; ""Chapter 6. The Drinfel'd Double""; ""6.1. The Drinfel'd double""; ""6.2. Factorizability""; ""6.3. The center of the character ring"" 327 $a""6.4. The third formula for the Frobenius-Schur indicators""""Chapter 7. Examples""; ""7.1. A class of extensions""; ""7.2. The coefficients""; ""7.3. Sweedler powers of the integral""; ""7.4. The simple modules""; ""7.5. Nonintegral indicators""; ""7.6. Noncocommutative Sweedler powers""; ""7.7. Noncentral Sweedler powers""; ""Bibliography""; ""Subject Index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""L""; ""M""; ""N""; ""O""; ""P""; ""R""; ""S""; ""T""; ""U""; ""V""; ""W""; ""Symbol Index"" 410 0$aMemoirs of the American Mathematical Society ;$vno. 855. 606 $aHopf algebras 606 $aLie superalgebras 606 $aFrobenius algebras 606 $aCauchy integrals 608 $aElectronic books. 615 0$aHopf algebras. 615 0$aLie superalgebras. 615 0$aFrobenius algebras. 615 0$aCauchy integrals. 676 $a510 s 676 $a512/.55 700 $aKashina$b Yevgenia$f1971-$0987763 702 $aSommerha?user$b Yorck$f1966- 702 $aZhu$b Yongchang 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910479856303321 996 $aOn higher Frobenius-Schur indicators$92258321 997 $aUNINA