Intermediate Subfactors
Author: Zeph A. Landau
Publisher:
Published: 1998
Total Pages: 288
ISBN-13:
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Kac Algebras Arising from Composition of Subfactors: General Theory and Classification
Author: Masaki Izumi
Publisher: American Mathematical Soc.
Published: 2002
Total Pages: 215
ISBN-13: 0821829351
DOWNLOAD EBOOKThis 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
Intermediate Subfactors with Small Index
Author: Pinhas Grossman
Publisher:
Published: 2006
Total Pages: 118
ISBN-13: 9780542824524
DOWNLOAD EBOOKWe approach the classification of intermediate subfactors by considering pairs of intermediate subfactors with index less than 4.
Introduction to Subfactors
Author: Vaughan F. R. Jones
Publisher: Cambridge University Press
Published: 1997-05-15
Total Pages: 178
ISBN-13: 0521584205
DOWNLOAD EBOOKSubfactors 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.
The Classification of Subfactors with Index at Most $5 frac {1}{4}$
Author: Narjess Afzaly
Publisher: American Mathematical Society
Published: 2023-04-07
Total Pages: 94
ISBN-13: 1470447126
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Quantum and Non-Commutative Analysis
Author: Huzihiro Araki
Publisher: Springer Science & Business Media
Published: 2013-04-17
Total Pages: 452
ISBN-13: 9401728232
DOWNLOAD EBOOKIn 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.
Normal Intermediate Subfactors
Author: Tamotsu Teruya
Publisher:
Published: 1995
Total Pages: 44
ISBN-13:
DOWNLOAD EBOOKOperator Algebras and Operator Theory
Author: Liming Ge
Publisher: American Mathematical Soc.
Published: 1998
Total Pages: 416
ISBN-13: 0821810936
DOWNLOAD EBOOKThis 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
Published: 1994-09-30
Total Pages: 306
ISBN-13: 981455071X
DOWNLOAD EBOOKThe 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.
Published:
Total Pages: 338
ISBN-13: 9780821871218
DOWNLOAD EBOOKThe 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?
