An Introduction To The Classification Of Amenable C Algebras
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| Author | : Huaxin Lin |
| Publisher | : World Scientific |
| Total Pages | : 333 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : 9810246803 |
The theory and applications of C?-algebras are related to fields ranging from operator theory, group representations and quantum mechanics, to non-commutative geometry and dynamical systems. By Gelfand transformation, the theory of C?-algebras is also regarded as non-commutative topology. About a decade ago, George A. Elliott initiated the program of classification of C?-algebras (up to isomorphism) by their K-theoretical data. It started with the classification of AT-algebras with real rank zero. Since then great efforts have been made to classify amenable C?-algebras, a class of C?-algebras that arises most naturally. For example, a large class of simple amenable C?-algebras is discovered to be classifiable. The application of these results to dynamical systems has been established.This book introduces the recent development of the theory of the classification of amenable C?-algebras ? the first such attempt. The first three chapters present the basics of the theory of C?-algebras which are particularly important to the theory of the classification of amenable C?-algebras. Chapter 4 otters the classification of the so-called AT-algebras of real rank zero. The first four chapters are self-contained, and can serve as a text for a graduate course on C?-algebras. The last two chapters contain more advanced material. In particular, they deal with the classification theorem for simple AH-algebras with real rank zero, the work of Elliott and Gong. The book contains many new proofs and some original results related to the classification of amenable C?-algebras. Besides being as an introduction to the theory of the classification of amenable C?-algebras, it is a comprehensive reference for those more familiar with the subject.
| Author | : Huaxin Lin |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 249 |
| Release | : 2017-08-11 |
| Genre | : Mathematics |
| ISBN | : 1470434903 |
This book examines some recent developments in the theory of -algebras, which are algebras of operators on Hilbert spaces. An elementary introduction to the technical part of the theory is given via a basic homotopy lemma concerning a pair of almost commuting unitaries. The book presents an outline of the background as well as some recent results of the classification of simple amenable -algebras, otherwise known as the Elliott program. This includes some stable uniqueness theorems and a revisiting of Bott maps via stable homotopy. Furthermore, -theory related rotation maps are introduced. The book is based on lecture notes from the CBMS lecture sequence at the University of Wyoming in the summer of 2015.
| Author | : Huaxin Lin |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 144 |
| Release | : 2010 |
| Genre | : Mathematics |
| ISBN | : 0821851942 |
"Volume 205, number 963 (second of 5 numbers)."
| Author | : Thierry Giordano |
| Publisher | : Springer |
| Total Pages | : 494 |
| Release | : 2018-08-28 |
| Genre | : Mathematics |
| ISBN | : 3319708694 |
This book collects the notes of the lectures given at an Advanced Course on Dynamical Systems at the Centre de Recerca Matemàtica (CRM) in Barcelona. The notes consist of four series of lectures. The first one, given by Andrew Toms, presents the basic properties of the Cuntz semigroup and its role in the classification program of simple, nuclear, separable C*-algebras. The second series of lectures, delivered by N. Christopher Phillips, serves as an introduction to group actions on C*-algebras and their crossed products, with emphasis on the simple case and when the crossed products are classifiable. The third one, given by David Kerr, treats various developments related to measure-theoretic and topological aspects of crossed products, focusing on internal and external approximation concepts, both for groups and C*-algebras. Finally, the last series of lectures, delivered by Thierry Giordano, is devoted to the theory of topological orbit equivalence, with particular attention to the classification of minimal actions by finitely generated abelian groups on the Cantor set.
| Author | : Karen R. Strung |
| Publisher | : Springer Nature |
| Total Pages | : 322 |
| Release | : 2020-12-15 |
| Genre | : Mathematics |
| ISBN | : 3030474658 |
This book is directed towards graduate students that wish to start from the basic theory of C*-algebras and advance to an overview of some of the most spectacular results concerning the structure of nuclear C*-algebras. The text is divided into three parts. First, elementary notions, classical theorems and constructions are developed. Then, essential examples in the theory, such as crossed products and the class of quasidiagonal C*-algebras, are examined, and finally, the Elliott invariant, the Cuntz semigroup, and the Jiang-Su algebra are defined. It is shown how these objects have played a fundamental role in understanding the fine structure of nuclear C*-algebras. To help understanding the theory, plenty of examples, treated in detail, are included. This volume will also be valuable to researchers in the area as a reference guide. It contains an extensive reference list to guide readers that wish to travel further.
| Author | : Rajendra Bhatia |
| Publisher | : World Scientific |
| Total Pages | : 4137 |
| Release | : 2011-06-06 |
| Genre | : Mathematics |
| ISBN | : 9814462934 |
ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.
| Author | : |
| Publisher | : World Scientific |
| Total Pages | : 1001 |
| Release | : |
| Genre | : |
| ISBN | : |
| Author | : Deguang Han |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 440 |
| Release | : 2006 |
| Genre | : Mathematics |
| ISBN | : 0821839233 |
This book offers a presentation of some new trends in operator theory and operator algebras, with a view to their applications. It consists of separate papers written by some of the leading practitioners in the field. The content is put together by the three editors in a way that should help students and working mathematicians in other parts of the mathematical sciences gain insight into an important part of modern mathematics and its applications. While different specialist authors are outlining new results in this book, the presentations have been made user friendly with the aid of tutorial material. In fact, each paper contains three things: a friendly introduction with motivation, tutorial material, and new research. The authors have strived to make their results relevant to the rest of mathematics. A list of topics discussed in the book includes wavelets, frames and their applications, quantum dynamics, multivariable operator theory, $C*$-algebras, and von Neumann algebras. Some longer papers present recent advances on particular, long-standing problems such as extensions and dilations, the Kadison-Singer conjecture, and diagonals of self-adjoint operators.
| Author | : |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 190 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 9780821839287 |
This volume contains translations of papers that originally appeared in the Japanese journal 'Sugaku'. The papers range over a variety of topics, including operator algebras, analysis, and statistics.
| Author | : Huaxin Lin |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 122 |
| Release | : 2015-04-09 |
| Genre | : Mathematics |
| ISBN | : 147041466X |
A unital separable -algebra, is said to be locally AH with no dimension growth if there is an integer satisfying the following: for any and any compact subset there is a unital -subalgebra, of with the form , where is a compact metric space with covering dimension no more than and is a projection, such that The authors prove that the class of unital separable simple -algebras which are locally AH with no dimension growth can be classified up to isomorphism by their Elliott invariant. As a consequence unital separable simple -algebras which are locally AH with no dimension growth are isomorphic to a unital simple AH-algebra with no dimension growth.
