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Crossed Products With Continuous Trace


Crossed Products With Continuous Trace
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Crossed Products With Continuous Trace


Crossed Products With Continuous Trace
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Author : Siegfried Echterhoff
language : en
Publisher: American Mathematical Soc.
Release Date : 1996

Crossed Products With Continuous Trace written by Siegfried Echterhoff and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.


This memoir presents an extensive study of strongly continuous actions of abelian locally compact groups on [italic capital]C*-algebras with continuous trace. Expositions of the Mackey-Green-Rieffel machine of induced representations and the theory of Morita equivalent [italic capital]C*-dynamical systems are included. There is also an elaboration of the representation theory of crossed products by actions of abelian groups on type I [italic capital]C*-algebras.



Crossed Products Of Continuous Trace C Algebras By Smooth Actions


Crossed Products Of Continuous Trace C Algebras By Smooth Actions
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Author : Mathematical Sciences Research Institute (Berkeley, Calif.).
language : en
Publisher:
Release Date : 1985

Crossed Products Of Continuous Trace C Algebras By Smooth Actions written by Mathematical Sciences Research Institute (Berkeley, Calif.). and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with categories.




Crossed Products Of C Algebras


Crossed Products Of C Algebras
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Author : Dana P. Williams
language : en
Publisher: American Mathematical Soc.
Release Date : 2007

Crossed Products Of C Algebras written by Dana P. Williams and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.


The theory of crossed products is extremely rich and intriguing. There are applications not only to operator algebras, but to subjects as varied as noncommutative geometry and mathematical physics. This book provides a detailed introduction to this vast subject suitable for graduate students and others whose research has contact with crossed product $C*$-algebras. in addition to providing the basic definitions and results, the main focus of this book is the fine ideal structure of crossed products as revealed by the study of induced representations via the Green-Mackey-Rieffel machine. in particular, there is an in-depth analysis of the imprimitivity theorems on which Rieffel's theory of induced representations and Morita equivalence of $C*$-algebras are based. There is also a detailed treatment of the generalized Effros-Hahn conjecture and its proof due to Gootman, Rosenberg, and Sauvageot. This book is meant to be self-contained and accessible to any graduate student coming out of a first course on operator algebras. There are appendices that deal with ancillary subjects, which while not central to the subject, are nevertheless crucial for a complete understanding of the material. Some of the appendices will be of independent interest. to view another book by this author, please visit Morita Equivalence and Continuous-Trace $C*$-Algebras.



Morita Equivalence And Continuous Trace C Algebras


Morita Equivalence And Continuous Trace C Algebras
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Author : Iain Raeburn
language : en
Publisher: American Mathematical Soc.
Release Date : 1998

Morita Equivalence And Continuous Trace C Algebras written by Iain Raeburn and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.


A modern treatment of this complex mathematical topic for students beginning research in operator algebras as well as mathematical physicists. Topics include the algebra of compact operators, sheaves, cohomology, the Brauer group and group actions, and the imprimivity theorem. The authors assume a knowledge of C*-algebras, the Gelfand-Naimark Theorem, continuous functional calculus, positivity, and the GNS- construction. Annotation copyrighted by Book News, Inc., Portland, OR



The Structure Of Crossed Product C Algebras


The Structure Of Crossed Product C Algebras
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Author : Philip Palmer Green
language : en
Publisher:
Release Date : 1976

The Structure Of Crossed Product C Algebras written by Philip Palmer Green and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with categories.




Crossed Products Of C Algebras Topological Dynamics And Classification


Crossed Products Of C Algebras Topological Dynamics And Classification
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Author : Thierry Giordano
language : en
Publisher: Springer
Release Date : 2018-08-28

Crossed Products Of C Algebras Topological Dynamics And Classification written by Thierry Giordano and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-28 with Mathematics categories.


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.



K Theory For Group C Algebras And Semigroup C Algebras


K Theory For Group C Algebras And Semigroup C Algebras
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Author : Joachim Cuntz
language : en
Publisher: Birkhäuser
Release Date : 2017-10-24

K Theory For Group C Algebras And Semigroup C Algebras written by Joachim Cuntz and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-24 with Mathematics categories.


This book gives an account of the necessary background for group algebras and crossed products for actions of a group or a semigroup on a space and reports on some very recently developed techniques with applications to particular examples. Much of the material is available here for the first time in book form. The topics discussed are among the most classical and intensely studied C*-algebras. They are important for applications in fields as diverse as the theory of unitary group representations, index theory, the topology of manifolds or ergodic theory of group actions. Part of the most basic structural information for such a C*-algebra is contained in its K-theory. The determination of the K-groups of C*-algebras constructed from group or semigroup actions is a particularly challenging problem. Paul Baum and Alain Connes proposed a formula for the K-theory of the reduced crossed product for a group action that would permit, in principle, its computation. By work of many hands, the formula has by now been verified for very large classes of groups and this work has led to the development of a host of new techniques. An important ingredient is Kasparov's bivariant K-theory. More recently, also the C*-algebras generated by the regular representation of a semigroup as well as the crossed products for actions of semigroups by endomorphisms have been studied in more detail. Intriguing examples of actions of such semigroups come from ergodic theory as well as from algebraic number theory. The computation of the K-theory of the corresponding crossed products needs new techniques. In cases of interest the K-theory of the algebras reflects ergodic theoretic or number theoretic properties of the action.



Superstrings Geometry Topology And C Algebras


Superstrings Geometry Topology And C Algebras
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Author : Robert S. Doran
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-10-13

Superstrings Geometry Topology And C Algebras written by Robert S. Doran and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-13 with Mathematics categories.


This volume contains the proceedings of an NSF-CBMS Conference held at Texas Christian University in Fort Worth, Texas, May 18-22, 2009. The papers, written especially for this volume by well-known mathematicians and mathematical physicists, are an outgrowth of the talks presented at the conference. Topics examined are highly interdisciplinary and include, among many other things, recent results on D-brane charges in $K$-homology and twisted $K$-homology, Yang-Mills gauge theory and connections with non-commutative geometry, Landau-Ginzburg models, $C^*$-algebraic non-commutative geometry and ties to quantum physics and topology, the rational homotopy type of the group of unitary elements in an Azumaya algebra, and functoriality properties in the theory of $C^*$-crossed products and fixed point algebras for proper actions. An introduction, written by Jonathan Rosenberg, provides an instructive overview describing common themes and how the various papers in the volume are interrelated and fit together. The rich diversity of papers appearing in the volume demonstrates the current interplay between superstring theory, geometry/topology, and non-commutative geometry. The book will be of interest to graduate students, mathematicians, mathematical physicists, and researchers working in these areas.



C Algebras


C Algebras
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Author : Joachim Cuntz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

C Algebras written by Joachim Cuntz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.


This book contains a collection of articles provided by the participants of the SFB-workshop on C*-algebras, March 8 - March 12, 1999 which was held at the Sonderforschungsbereich "Geometrische Strukturen in der reinen Mathematik" of the University of Münster, Germany. The aim of the workshop was to bring together leading experts in the theory of C* -algebras with promising young researchers in the field, and to provide a stimulating atmosphere for discussions and interactions between the participants. There were 19 one-hour lectures on various topics like - classification of nuclear C* -algebras, - general K-theory for C* -algebras, - exact C* -algebras and exact groups, - C*-algebras associated to (infinite) matrices and C*-correspondences, - noncommutative prob ability theory, - deformation quantization, - group C* -algebras and the Baum-Connes conjecture, giving a broad overview of the latest developments in the field, and serving as a basis for discussions. We, the organizers of the workshop, were greatly pleased with the excellence of the lectures and so were led to the idea of publishing the proceedings of the conference. There are basically two kinds of contributions. On one side there are several articles giving surveys and overviews on new developments and im portant results of the theory, on the other side one finds original articles with interesting new results.



Advances In Invariant Subspaces And Other Results Of Operator Theory


Advances In Invariant Subspaces And Other Results Of Operator Theory
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Author : Arsene
language : en
Publisher: Birkhäuser
Release Date : 2013-11-11

Advances In Invariant Subspaces And Other Results Of Operator Theory written by Arsene and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.


The annual Operator Theory conferences, organized by the Department of Mathematics of INC REST and the University of Timi?oara, are intended to promote cooperation and exchange of information between specialists in all areas of operator theory. This volume consists of papers contributed by the participants of the 1984 Conference. They reflect a great variety of topics, dealt with by the modern operator theory, including very recent advances in the invariant subspace problem, subalgebras of operator algebras, hyponormal, Hankel and other special classes of operators, spectral decompositions, aspects of dilation theory and so on. The research contracts of the Department of Mathematics of INCREST with the National Council for Science and Technology of Romania provided the means for developing the research activity in mathematics; they represent the generous framework of these meetings, too. It is our pleasure to acknowledge the financial support of UNESCO which also contibuted to the success of this meeting. We are indebted to Professor Israel Gohberg for including these Proceedings in the OT Series and for valuable advice in the editing process. Birkhauser Verlag was very cooperative in publishing this volume. Mariana Bota, Camelia Minculescu and Rodica Stoenescu dealt with the difficult task of typing the whole manuscript using a Rank Xerox 860 word processor; we thank them for the excellent job they did.