ORPP logo
Image from Google Jackets

Kac Algebras Arising from Composition of Subfactors : General Theory and Classification.

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical SocietyPublisher: Providence : American Mathematical Society, 2002Copyright date: ©2002Edition: 1st edDescription: 1 online resource (215 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781470403430
Subject(s): Genre/Form: Additional physical formats: Print version:: Kac Algebras Arising from Composition of SubfactorsDDC classification:
  • 510 s;512/.55
LOC classification:
  • QA252.3 -- .I98 2002eb
Online resources:
Contents:
Intro -- 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(θ)] -- Chapter 4. Multiplicative unitary -- 1. Preliminaries -- 2. Orthonormal basis and multiplicative unitary -- Chapter 5. Kac algebra structure -- Chapter 6. Group-like elements -- Chapter 7. Examples of finite-dimensional Kac algebras -- 1. (Z[sub(n)] x Z[sub(n)]) x Z[sub(2)] with n ≥ 3 -- 2. (Z[sub(2)] x Z[sub(2)]) x Z[sub(2)] -- 3. (Z[sub(n)] x Z[sub(n)]) x Z[sub(2)] with n ≥ 2 -- 4. (Z[sub(n)] x Z[sub(n)]) x Z[sub(2)] with n even -- 5. D[sub(2n)] x Z[sub(2)] with n odd -- 6. D[sub(2n)] x Z[sub(2)] with n even -- Chapter 8. Inclusions with the Coxeter-Dynkin graph D[sup((1))][sub(6)] and the Kac-Paljutkin algebra -- 1. The group of one-dimensional sectors -- 2. Kac-Paljutkin algebra -- 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.
Tags from this library: No tags from this library for this title. Log in to add tags.
Star ratings
    Average rating: 0.0 (0 votes)
No physical items for this record

Intro -- 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(θ)] -- Chapter 4. Multiplicative unitary -- 1. Preliminaries -- 2. Orthonormal basis and multiplicative unitary -- Chapter 5. Kac algebra structure -- Chapter 6. Group-like elements -- Chapter 7. Examples of finite-dimensional Kac algebras -- 1. (Z[sub(n)] x Z[sub(n)]) x Z[sub(2)] with n ≥ 3 -- 2. (Z[sub(2)] x Z[sub(2)]) x Z[sub(2)] -- 3. (Z[sub(n)] x Z[sub(n)]) x Z[sub(2)] with n ≥ 2 -- 4. (Z[sub(n)] x Z[sub(n)]) x Z[sub(2)] with n even -- 5. D[sub(2n)] x Z[sub(2)] with n odd -- 6. D[sub(2n)] x Z[sub(2)] with n even -- Chapter 8. Inclusions with the Coxeter-Dynkin graph D[sup((1))][sub(6)] and the Kac-Paljutkin algebra -- 1. The group of one-dimensional sectors -- 2. Kac-Paljutkin algebra -- 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.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

There are no comments on this title.

to post a comment.

© 2024 Resource Centre. All rights reserved.