Overview

This EMS volume consists of two parts, written by leading scientists in the field of operator algebras and non-commutative geometry. The first part, written by M.Rordam, is on Elliott's classification program for nuclear C*-algebras. The emphasis is on the work of Kirchberg and the spectacular results by Kirchberg and Phillips giving a nearly complete classification, in terms of K-theoretic invariants, in the purely infinite case. This part of the program is described with almost full proofs beginning with Kirchberg's tensor product theorems and Kirchberg's embedding theorem for exact C*-algebras. The classification of finite simple C*-algebras starting with AF-algebras, and continuing with AT- and AH-algebras is covered, but mostly without proofs. The second part, written by E.Stormer, is a survey of the theory of of noncommutative entropy of automorphisms of C*-algebras and von Neumann algebras from its initiation by Connes and Stormer in 1975 till 2001.

Full Product Details

Author:   M. Rordam ,  E. Stormer
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   2002 ed.
Volume:   126
Dimensions:   Width: 15.50cm , Height: 1.20cm , Length: 23.50cm
Weight:   1.050kg
ISBN:  

9783540423058

ISBN 10:   3540423052
Pages:   198
Publication Date:   20 November 2001
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD  
We will order this item for you from a manufatured on demand supplier.

Table of Contents

Part I. Classification of Nuclear, Simple C*-Algebras, M.Rordam: 1. AF-algebras and their Classification.- 2. Preliminaries.- 3. Classification results for finite C*-algebras.- 4. Purely infinite simple C*-algebras.- 5. On O 2.- 6. Nuclear and exact C*-algebras and exact C*-algebras.- 7. Tensor products by O 2 and O Öinfty.- 8. Classification of Kirchberg algebras.- Part II. A Survey of Noncommutative Dynamical Entropy, E. Stormer: Introduction.- 1. Entropy in finite von Neumann algebras.- 2. Entropy in C*-algebras.- 3. Bogoliubov automorphisms.- 4. The entropy of Sauvageot and Thouvenot.- 5. Voiculescu's approximation entropies.- 6. Crossed products.- 7. Free products.- 8. Binary shifts.- 9. Generators.- 10. The variational principle.

Reviews

.,. These notes [by E.Stormer] describe the main approaches to noncommutative entropy, together with several ramifications and variants. The notion of generator and variational principle are used to give applications to subfactors and C*-algebra formalism of quantum statistical mechanics. The author considers the most frequently studied examples, including Bernoulli shifts, Bogolyubov automorphisms, dual automorphisms on crossed products, shifts on infinite free products, and binary shifts on the CAR-algebra. The mathematical techniques and ideas are beautifully exposed, and the whole paper is a rich resource on the subject, either for the expert or the beginner. ... <p>V.Deaconu, Mathematical Reviews 2004 <p>.,. the author gives a clear presentation of the dramatic developments in the classification theory for simple C*-algebras that have taken place over the past 25 years or so. ... As there is such a large amount of literature on the subject, this monograph article is particularly useful to the relative novice who wants to know the fundamental results in the theory without wading through a massive amount of detail. ...This monograph-length article is extremely well-written, filled with concrete examples, and has an exhaustive bibliography. I recommend it as an excellent introduction to graduate students and other mathematicians who want to bring themselves up-to-date on the subject. .. <p>J.A.Packer, Mathematical Reviews 2004 <p>

... These notes [by E.Stormer] describe the main approaches to noncommutative entropy, together with several ramifications and variants. The notion of generator and variational principle are used to give applications to subfactors and C*-algebra formalism of quantum statistical mechanics. The author considers the most frequently studied examples, including Bernoulli shifts, Bogolyubov automorphisms, dual automorphisms on crossed products, shifts on infinite free products, and binary shifts on the CAR-algebra. The mathematical techniques and ideas are beautifully exposed, and the whole paper is a rich resource on the subject, either for the expert or the beginner. ... V.Deaconu, Mathematical Reviews 2004 ... the author gives a clear presentation of the dramatic developments in the classification theory for simple C*-algebras that have taken place over the past 25 years or so. ... As there is such a large amount of literature on the subject, this monograph article is particularly useful to the relative novice who wants to know the fundamental results in the theory without wading through a massive amount of detail. ...This monograph-length article is extremely well-written, filled with concrete examples, and has an exhaustive bibliography. I recommend it as an excellent introduction to graduate students and other mathematicians who want to bring themselves up-to-date on the subject. .. J.A.Packer, Mathematical Reviews 2004

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