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Equivariant K Theory And Freeness Of Group Actions On C Algebras
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Book Synopsis Equivariant K-Theory and Freeness of Group Actions on C*-Algebras by : N. Christopher Phillips
Download or read book Equivariant K-Theory and Freeness of Group Actions on C*-Algebras written by N. Christopher Phillips and published by Springer. This book was released on 2006-11-15 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Freeness of an action of a compact Lie group on a compact Hausdorff space is equivalent to a simple condition on the corresponding equivariant K-theory. This fact can be regarded as a theorem on actions on a commutative C*-algebra, namely the algebra of continuous complex-valued functions on the space. The successes of "noncommutative topology" suggest that one should try to generalize this result to actions on arbitrary C*-algebras. Lacking an appropriate definition of a free action on a C*-algebra, one is led instead to the study of actions satisfying conditions on equivariant K-theory - in the cases of spaces, simply freeness. The first third of this book is a detailed exposition of equivariant K-theory and KK-theory, assuming only a general knowledge of C*-algebras and some ordinary K-theory. It continues with the author's research on K-theoretic freeness of actions. It is shown that many properties of freeness generalize, while others do not, and that certain forms of K-theoretic freeness are related to other noncommutative measures of freeness, such as the Connes spectrum. The implications of K-theoretic freeness for actions on type I and AF algebras are also examined, and in these cases K-theoretic freeness is characterized analytically.
Book Synopsis Equivariant K-theory and Freeness of Group Actions on C-algebras by : N. Christopher Philipps
Download or read book Equivariant K-theory and Freeness of Group Actions on C-algebras written by N. Christopher Philipps and published by . This book was released on 1987 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Equivariant $E$-Theory for $C^*$-Algebras by : Erik Guentner
Download or read book Equivariant $E$-Theory for $C^*$-Algebras written by Erik Guentner and published by American Mathematical Soc.. This book was released on 2000 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title examines the equivariant e-theory for c*-algebra, focusing on research carried out by Higson and Kasparov. Let A and B be C*-algebras which are equipped with continuous actions of a second countable, locally compact group G. We define a notion of equivariant asymptotic morphism, and use it to define equivariant E-theory groups EULG(A, B) which generalize the E-theory groups of Connes and Higson. We develop the basic properties of equivariant E-theory, including a composition product and six-term exact sequences in both variables, and apply our theory to the problem of calculating K-theory for group C*-algebras. Our main theorem gives a simple criterion for the assembly map of Baum and Connes to be an isomorphism. The result plays an important role in the work of Higson and Kasparov on the Bau m-Connes conjecture for groups which act isometrically and metrically properly on Hilbert space
Book Synopsis Index Theory of Elliptic Operators, Foliations, and Operator Algebras by : Jerome Kaminker
Download or read book Index Theory of Elliptic Operators, Foliations, and Operator Algebras written by Jerome Kaminker and published by American Mathematical Soc.. This book was released on 1988 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combining analysis, geometry, and topology, this volume provides an introduction to current ideas involving the application of $K$-theory of operator algebras to index theory and geometry. In particular, the articles follow two main themes: the use of operator algebras to reflect properties of geometric objects and the application of index theory in settings where the relevant elliptic operators are invertible modulo a $C^*$-algebra other than that of the compact operators. The papers in this collection are the proceedings of the special sessions held at two AMS meetings: the Annual meeting in New Orleans in January 1986, and the Central Section meeting in April 1986. Jonathan Rosenberg's exposition supplies the best available introduction to Kasparov's $KK$-theory and its applications to representation theory and geometry. A striking application of these ideas is found in Thierry Fack's paper, which provides a complete and detailed proof of the Novikov Conjecture for fundamental groups of manifolds of non-positive curvature. Some of the papers involve Connes' foliation algebra and its $K$-theory, while others examine $C^*$-algebras associated to groups and group actions on spaces.
Book Synopsis Group Actions on Rings by : Susan Montgomery
Download or read book Group Actions on Rings written by Susan Montgomery and published by American Mathematical Soc.. This book was released on 1985 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ring theorists and researchers in invariant theory and operator algebra met at Bowdoin for the 1984 AMS-IMS-SIAM Joint Summer Research Conference to exchange ideas about group actions on rings. This work discusses topics common to the three fields, including: $K$-theory, dual actions, semi-invariants and crossed products.
Book Synopsis K-Theory for Operator Algebras by : Bruce Blackadar
Download or read book K-Theory for Operator Algebras written by Bruce Blackadar and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: K -Theory has revolutionized the study of operator algebras in the last few years. As the primary component of the subject of "noncommutative topol ogy," K -theory has opened vast new vistas within the structure theory of C* algebras, as well as leading to profound and unexpected applications of opera tor algebras to problems in geometry and topology. As a result, many topolo gists and operator algebraists have feverishly begun trying to learn each others' subjects, and it appears certain that these two branches of mathematics have become deeply and permanently intertwined. Despite the fact that the whole subject is only about a decade old, operator K -theory has now reached a state of relative stability. While there will undoubtedly be many more revolutionary developments and applications in the future, it appears the basic theory has more or less reached a "final form." But because of the newness of the theory, there has so far been no comprehensive treatment of the subject. It is the ambitious goal of these notes to fill this gap. We will develop the K -theory of Banach algebras, the theory of extensions of C*-algebras, and the operator K -theory of Kasparov from scratch to its most advanced aspects. We will not treat applications in detail; however, we will outline the most striking of the applications to date in a section at the end, as well as mentioning others at suitable points in the text.
Book Synopsis Operator Algebras by : Bruce Blackadar
Download or read book Operator Algebras written by Bruce Blackadar and published by Taylor & Francis. This book was released on 2006 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive introduction to the general theory of C*-algebras and von Neumann algebras. Beginning with the basics, the theory is developed through such topics as tensor products, nuclearity and exactness, crossed products, K-theory, and quasidiagonality. The presentation carefully and precisely explains the main features of each part of the theory of operator algebras; most important arguments are at least outlined and many are presented in full detail.
Book Synopsis Mappings of Operator Algebras by : Araki, Takeo
Download or read book Mappings of Operator Algebras written by Araki, Takeo and published by Springer Science & Business Media. This book was released on 1991 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: On Convex Combinations of Unitary Operators in C*-Algebras.- Approximately Inner Derivations, Decompositions and Vector Fields of Simple C*-Algebras.- Derivations in Commutative C*-Algebras.- Representation of Quantum Groups.- Automorphism Groups and Covariant Irreducible Representations.- Proper Actions of Groups on C*-Algebras.- On the Baum-Connes Conjecture.- On Primitive Ideal Spaces of C*-Algebras over Certain Locally Compact Groupoids.- On Sequences of Jones' Projections.- The Powers' Binary Shifts on the Hyperfinite Factor of Type II1.- Index Theory for Type III Factors.- Relative Entropy of a Fixed Point Algebra.- Jones Index Theory for C*-Algebras.- Three Tensor Norms for Operator Spaces.- Extension Problems for Maps on Operator Systems.- Multivariable Toeplitz Operators and Index Theory.- On Maximality of Analytic Subalgebras Associated with Flow in von Neumann Algebras.- Reflections Relating a von Neumann Algebra and Its Commutant.- Normal AW*-Algebras.
Book Synopsis Operator Structures and Dynamical Systems by : Marcel de Jeu
Download or read book Operator Structures and Dynamical Systems written by Marcel de Jeu and published by American Mathematical Soc.. This book was released on 2009-11-30 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of a Leiden Workshop on Dynamical Systems and their accompanying Operator Structures which took place at the Lorentz Center in Leiden, The Netherlands, on July 21-25, 2008. These papers offer a panorama of selfadjoint and non-selfadjoint operator algebras associated with both noncommutative and commutative (topological) dynamical systems and related subjects. Papers on general theory, as well as more specialized ones on symbolic dynamics and complex dynamical systems, are included.
Book Synopsis Crossed Products of C*-Algebras, Topological Dynamics, and Classification by : Thierry Giordano
Download or read book Crossed Products of C*-Algebras, Topological Dynamics, and Classification written by Thierry Giordano and published by Springer. This book was released on 2018-08-28 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Operator Algebras and Applications: Volume 1, Structure Theory; K-theory, Geometry and Topology by : David E. Evans
Download or read book Operator Algebras and Applications: Volume 1, Structure Theory; K-theory, Geometry and Topology written by David E. Evans and published by Cambridge University Press. This book was released on 1988 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: These volumes form an authoritative statement of the current state of research in Operator Algebras. They consist of papers arising from a year-long symposium held at the University of Warwick. Contributors include many very well-known figures in the field.
Book Synopsis Selfadjoint and Nonselfadjoint Operator Algebras and Operator Theory by : Robert S. Doran
Download or read book Selfadjoint and Nonselfadjoint Operator Algebras and Operator Theory written by Robert S. Doran and published by American Mathematical Soc.. This book was released on 1991 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains papers presented at the NSF/CBMS Regional Conference on Coordinates in Operator Algebras, held at Texas Christian University in Fort Worth in May 1990. During the conference, in addition to a series of ten lectures by Paul S Muhly (which will be published in a CBMS Regional Conference Series volume), there were twenty-eight lectures delivered by conference participants on a broad range of topics of current interest in operator algebras and operator theory. This volume contains slightly expanded versions of most of those lectures. Participants were encouraged to bring open problems to the conference, and, as a result, there are over one hundred problems and questions scattered throughout this volume. Readers will appreciate this book for the overview it provides of current topics and methods of operator algebras and operator theory.
Book Synopsis Superstrings, Geometry, Topology, and $C^*$-algebras by : Robert S. Doran
Download or read book Superstrings, Geometry, Topology, and $C^*$-algebras written by Robert S. Doran and published by American Mathematical Soc.. This book was released on 2010-10-13 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis K-theory and Homological Algebra by : Hvedri Inassaridze
Download or read book K-theory and Homological Algebra written by Hvedri Inassaridze and published by Springer. This book was released on 2006-11-14 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis C*-Algebras and Their Automorphism Groups by : Søren Eilers
Download or read book C*-Algebras and Their Automorphism Groups written by Søren Eilers and published by Academic Press. This book was released on 2018-08-08 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: This elegantly edited landmark edition of Gert Kjærgård Pedersen's C*-Algebras and their Automorphism Groups (1979) carefully and sensitively extends the classic work to reflect the wealth of relevant novel results revealed over the past forty years. Revered from publication for its writing clarity and extremely elegant presentation of a vast space within operator algebras, Pedersen's monograph is notable for reviewing partially ordered vector spaces and group automorphisms in unusual detail, and by strict intention releasing the C*-algebras from the yoke of representations as Hilbert space operators. Under the editorship of Søren Eilers and Dorte Olesen, the second edition modernizes Pedersen's work for a new generation of C*-algebraists, with voluminous new commentary, all-new indexes, annotation and terminology annexes, and a surfeit of new discussion of applications and of the author's later work. - Covers basic C*-algebras theory in a short and appealingly elegant way, with a few additions and corrections given to the editors by the original author - Expands coverage to select contemporary accomplishments in C*-algebras of direct relevance to the scope of the first edition, including aspects of K-theory and set theory - Identifies key modern literature in an updated bibliography with over 100 new entries, and greatly enhances indexing throughout - Modernizes coverage of algebraic problems in relation to the theory of unitary representations of locally compact groups - Reviews mathematical accomplishments of Gert K. Pedersen in comments and a biography
Book Synopsis Canadian Journal of Mathematics by :
Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1989-12 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Structured Ring Spectra by : Andrew Baker
Download or read book Structured Ring Spectra written by Andrew Baker and published by Cambridge University Press. This book was released on 2004-11-18 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains some important new contributions to the theory of structured ring spectra.
