03491nam 2200565 450 991081275000332120180613001303.01-4704-0343-9(CKB)3360000000464934(EBL)3114436(SSID)ssj0000973265(PQKBManifestationID)11537967(PQKBTitleCode)TC0000973265(PQKBWorkID)10959360(PQKB)10751075(MiAaPQ)EBC3114436(RPAM)12687446(PPN)195416368(EXLCZ)99336000000046493420020226h20022002 uy| 0engur|n|---|||||txtccrKac algebras arising from composition of subfactors general theory and classification /Masaki Izumi, Hideki KsakiProvidence, Rhode Island :American Mathematical Society,[2002]©20021 online resource (215 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 750Description based upon print version of record.0-8218-2935-1 Includes bibliographical references and index.""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Actions of matched pairs""; ""1. Cocycles and cohomology group""; ""2. Cocycle conjugacy""; ""3. Appendix Iterated perturbation""; ""4. Appendix Normalization of cocycles""; ""Chapter 3. Cocycles attached to the pentagon equation""; ""1. Cocycles""; ""2. Cohomology group""; ""3. Appendix Normalization of cocycles""; ""4. Appendix Multiplicative unitary V[sup(Î?)]""; ""Chapter 4. Multiplicative unitary""; ""1. Preliminaries""; ""2. Orthonormal basis and multiplicative unitary""; ""Chapter 5. Kac algebra structure""""Chapter 9. Structure theorems""""1. Preliminaries""; ""2. Main theorem""; ""3. Proof""; ""Chapter 10. Classification of certain Kac algebras""; ""1. Useful criteria""; ""2. 3p theorem""; ""3. p[sup(2)]q case""; ""4. Classification of low dimensional Kac algebras""; ""Chapter 11. Classification of Kac algebras of dimension 16""; ""1. Case when G(A) is an abelian group of order 8""; ""2. Computation of the invariant H[sup(2)]((D[sub(8)],Z[sub(2)]), T )/~""; ""3. Classification""; ""Chapter 12. Group extensions of general Kac algebras""; ""1. Description of cocycles""""2. Multiplicative unitary""""Chapter 13. 2-cocycles of Kac algebras""; ""1. Preliminaries""; ""2. Ergodic actions and 2-cocycles""; ""3. Examples I Kac-Paljutkin algebra""; ""4. Examples II Group algebras""; ""Chapter 14. Classification of Kac algebras of dimension 24""; ""1. Preliminaries""; ""2. Computation of H[sup(2)]((N, H), T )/~""; ""3. Reduction to the semi-direct product case""; ""4. Classification""; ""Bibliography""; ""Index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""J""; ""K""; ""M""; ""N""; ""O""; ""P""; ""Q""; ""R""; ""S""; ""T""; ""U""; ""W""; ""Z""Memoirs of the American Mathematical Society ;no. 750.Kac-Moody algebrasKac-Moody algebras.510 s512/.55Izumi Masaki1965-1619724Kosaki HidekiMiAaPQMiAaPQMiAaPQBOOK9910812750003321Kac algebras arising from composition of subfactors3952116UNINA