03664nam 2200649 450 991047985630332120170822144306.01-4704-0459-1(CKB)3360000000465039(EBL)3114251(SSID)ssj0000889108(PQKBManifestationID)11523069(PQKBTitleCode)TC0000889108(PQKBWorkID)10875533(PQKB)11642747(MiAaPQ)EBC3114251(PPN)195417437(EXLCZ)99336000000046503920060111h20062006 uy| 0engur|n|---|||||txtccrOn higher Frobenius-Schur indicators /Yevgenia Kashina, Yorck Sommerhäuser, Yongchang ZhuProvidence, Rhode Island :American Mathematical Society,[2006]©20061 online resource (82 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 855"Volume 181, number 855 (fourth of 5 numbers)."0-8218-3886-5 Includes bibliographical references (pages 59-60) and indexes.""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""""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""""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""Memoirs of the American Mathematical Society ;no. 855.Hopf algebrasLie superalgebrasFrobenius algebrasCauchy integralsElectronic books.Hopf algebras.Lie superalgebras.Frobenius algebras.Cauchy integrals.510 s512/.55Kashina Yevgenia1971-987763Sommerhäuser Yorck1966-Zhu YongchangMiAaPQMiAaPQMiAaPQBOOK9910479856303321On higher Frobenius-Schur indicators2258321UNINA