Intermediate Subfactors
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Kac Algebras Arising from Composition of Subfactors: General Theory and Classification
| Author | : Masaki Izumi |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 215 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 0821829351 |
This title deals with a map $\alpha$ from a finite group $G$ into the automorphism group $Aut({\mathcal L})$ of a factor ${\mathcal L}$ satisfying (i) $G=N \rtimes H$ is a semi-direct product, (ii) the induced map $g \in G \to [\alpha_g] \in Out({\mathcal L})=Aut({\mathcal L})/Int({\mathcal L})$ is an injective homomorphism, and (iii) the restrictions $\alpha \! \! \mid_N, \alpha \! \! \mid_H$ are genuine actions of the subgroups on the factor ${\mathcal L}$. The pair ${\mathcal M}={\mathcal L} \rtimes_{\alpha} H \supseteq {\mathcal N}={\mathcal L} DEGREES{\alpha\mid_N}$ (of the crossed product ${\mathcal L} \rtimes_{\alpha} H$ and the fixed-point algebra ${\mathcal L} DEGREES{\alpha\mid_N}$) gives an irreducible inclusion of factors with Jones index $\# G$. The inclusion ${\mathcal M} \supseteq {\mathcal N}$ is of depth $2$ and hence known to correspond to a Kac algebra of dim
The Classification of Subfactors with Index at Most $5 frac {1}{4}$
| Author | : Narjess Afzaly |
| Publisher | : American Mathematical Society |
| Total Pages | : 94 |
| Release | : 2023-04-07 |
| Genre | : Mathematics |
| ISBN | : 1470447126 |
View the abstract.
Introduction to Subfactors
| Author | : Vaughan F. R. Jones |
| Publisher | : Cambridge University Press |
| Total Pages | : 178 |
| Release | : 1997-05-15 |
| Genre | : Mathematics |
| ISBN | : 0521584205 |
Subfactors have been a subject of considerable research activity for about 15 years and are known to have significant relations with other fields such as low dimensional topology and algebraic quantum field theory. These notes give an introduction to the subject suitable for a student who has only a little familiarity with the theory of Hilbert space. A new pictorial approach to subfactors is presented in a late ch apter.
Quantum and Non-Commutative Analysis
| Author | : Huzihiro Araki |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 452 |
| Release | : 2013-04-17 |
| Genre | : Science |
| ISBN | : 9401728232 |
In the past decade, there has been a sudden and vigorous development in a number of research areas in mathematics and mathematical physics, such as theory of operator algebras, knot theory, theory of manifolds, infinite dimensional Lie algebras and quantum groups (as a new topics), etc. on the side of mathematics, quantum field theory and statistical mechanics on the side of mathematical physics. The new development is characterized by very strong relations and interactions between different research areas which were hitherto considered as remotely related. Focussing on these new developments in mathematical physics and theory of operator algebras, the International Oji Seminar on Quantum Analysis was held at the Kansai Seminar House, Kyoto, JAPAN during June 25-29, 1992 by a generous sponsorship of the Japan Society for the Promotion of Science and the Fujihara Foundation of Science, as a workshop of relatively small number of (about 50) invited participants. This was followed by an open Symposium at RIMS, described below by its organizer, A. Kishimoto. The Oji Seminar began with two key-note addresses, one by V.F.R. Jones on Spin Models in Knot Theory and von Neumann Algebras and by A. Jaffe on Where Quantum Field Theory Has Led. Subsequently topics such as Subfactors and Sector Theory, Solvable Models of Statistical Mechanics, Quantum Field Theory, Quantum Groups, and Renormalization Group Ap proach, are discussed. Towards the end, a panel discussion on Where Should Quantum Analysis Go? was held.
Operator Algebras and Operator Theory
| Author | : Liming Ge |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 416 |
| Release | : 1998 |
| Genre | : Mathematics |
| ISBN | : 0821810936 |
This volume contains the proceedings from the International Conference on Operator Algebras and Operator Theory held at the East China Normal University in Shanghai (China). Participants in the conference ranged from graduate students to postdocs to leading experts who came from around the world. Topics covered were $C*$-algebras, von Neumann algebras, non-self-adjoint operator algebras, wavelets, operator spaces and other related areas. This work consists of contributions from invited speakers and some mathematicians who were unable to attend. It presents important mathematical ideas while maintaining the uniqueness and excitement of this very successful event.
Subfactors: Proceedings Of The Taniguchi Symposium On Operator Algebras
| Author | : Huzihiro Araki |
| Publisher | : World Scientific |
| Total Pages | : 306 |
| Release | : 1994-09-30 |
| Genre | : |
| ISBN | : 981455071X |
The theory of subfactors of von Neumann algebras made an amazing development in the past ten years or so. In order to appraise the present state of the art in subfactor theory and to look for promising directions of future research, the workshop was organised. This workshop gives an overview of the foremost developments in subfactor theory and related topics.
Operator Algebras and Their Applications
| Author | : Peter A. Fillmore |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 338 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : 9780821871218 |
The study of operator algebras, which grew out of von Neumann's work in the 1920s and the 1930s on modelling quantum mechanics, has in recent years experienced tremendous growth and vitality. This growth has resulted in significant applications in other areas - both within and outside mathematics. The field was a natural candidate for a 1994-1995 program year in Operator Algebras and Applications held at The Fields Institute for Research in the Mathematical Sciences. This volume contains a selection of papers that arose from the seminars and workshops of the program. Topics covered include the classification of amenable C*-algebras, the Baum-Connes conjecture, E[subscript 0] semigroups, subfactors, E-theory, quasicrystals, and the solution to a long-standing problem in operator theory: Can almost commuting self-adjoint matrices be approximated by commuting self-adjoint matrices?
Operator Algebras
| Author | : Ola Bratteli |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 280 |
| Release | : 2007-01-19 |
| Genre | : Mathematics |
| ISBN | : 3540341978 |
The theme of the first Abel Symposium was operator algebras in a wide sense. In the last 40 years operator algebras have developed from a rather special discipline within functional analysis to become a central field in mathematics often described as "non-commutative geometry". It has branched out in several sub-disciplines and made contact with other subjects. The contributions to this volume give a state-of-the-art account of some of these sub-disciplines and the variety of topics reflect to some extent how the subject has developed. This is the first volume in a prestigious new book series linked to the Abel prize.
