C Algebra Extensions And K Homology
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Author |
: Ronald G. Douglas |
Publisher |
: Princeton University Press |
Total Pages |
: 96 |
Release |
: 2016-03-02 |
ISBN-10 |
: 9781400881468 |
ISBN-13 |
: 1400881463 |
Rating |
: 4/5 (68 Downloads) |
Synopsis C*-Algebra Extensions and K-Homology. (AM-95), Volume 95 by : Ronald G. Douglas
Recent developments in diverse areas of mathematics suggest the study of a certain class of extensions of C*-algebras. Here, Ronald Douglas uses methods from homological algebra to study this collection of extensions. He first shows that equivalence classes of the extensions of the compact metrizable space X form an abelian group Ext (X). Second, he shows that the correspondence X ⃗ Ext (X) defines a homotopy invariant covariant functor which can then be used to define a generalized homology theory. Establishing the periodicity of order two, the author shows, following Atiyah, that a concrete realization of K-homology is obtained.
Author |
: Ronald G. Douglas |
Publisher |
: |
Total Pages |
: 83 |
Release |
: 1980 |
ISBN-10 |
: 0691082650 |
ISBN-13 |
: 9780691082653 |
Rating |
: 4/5 (50 Downloads) |
Synopsis C*-algebra Extensions and K-homology by : Ronald G. Douglas
Recent developments in diverse areas of mathematics suggest the study of a certain class of extensions of C*-algebras. Here, Ronald Douglas uses methods from homological algebra to study this collection of extensions. He first shows that equivalence classes of the extensions of the compact metrizable space X form an abelian group Ext (X). Second, he shows that the correspondence X ⃗ Ext (X) defines a homotopy invariant covariant functor which can then be used to define a generalized homology theory. Establishing the periodicity of order two, the author shows, following Atiyah, that a concrete realization of K-homology is obtained.
Author |
: Ronald G. Douglas |
Publisher |
: Princeton University Press |
Total Pages |
: 112 |
Release |
: 1980-07-21 |
ISBN-10 |
: 0691082669 |
ISBN-13 |
: 9780691082660 |
Rating |
: 4/5 (69 Downloads) |
Synopsis C*-algebra Extensions and K-homology by : Ronald G. Douglas
Recent developments in diverse areas of mathematics suggest the study of a certain class of extensions of C*-algebras. Here, Ronald Douglas uses methods from homological algebra to study this collection of extensions. He first shows that equivalence classes of the extensions of the compact metrizable space X form an abelian group Ext (X). Second, he shows that the correspondence X ⃗ Ext (X) defines a homotopy invariant covariant functor which can then be used to define a generalized homology theory. Establishing the periodicity of order two, the author shows, following Atiyah, that a concrete realization of K-homology is obtained.
Author |
: Nigel Higson |
Publisher |
: OUP Oxford |
Total Pages |
: 426 |
Release |
: 2000-12-07 |
ISBN-10 |
: 9780191589201 |
ISBN-13 |
: 0191589209 |
Rating |
: 4/5 (01 Downloads) |
Synopsis Analytic K-Homology by : Nigel Higson
Analytic K-homology draws together ideas from algebraic topology, functional analysis and geometry. It is a tool - a means of conveying information among these three subjects - and it has been used with specacular success to discover remarkable theorems across a wide span of mathematics. The purpose of this book is to acquaint the reader with the essential ideas of analytic K-homology and develop some of its applications. It includes a detailed introduction to the necessary functional analysis, followed by an exploration of the connections between K-homology and operator theory, coarse geometry, index theory, and assembly maps, including a detailed treatment of the Atiyah-Singer Index Theorem. Beginning with the rudiments of C* - algebra theory, the book will lead the reader to some central notions of contemporary research in geometric functional analysis. Much of the material included here has never previously appeared in book form.
Author |
: Huaxin Lin |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 102 |
Release |
: 1995 |
ISBN-10 |
: 9780821826119 |
ISBN-13 |
: 0821826115 |
Rating |
: 4/5 (19 Downloads) |
Synopsis $C^*$-Algebra Extensions of $C(X)$ by : Huaxin Lin
We show that the Weyl-von Neumann theorem for unitaries holds for [lowercase Greek]Sigma-unital [italic capital]A[italic capital]F-algebras and their multiplier algebras.
Author |
: M. Rørdam |
Publisher |
: Cambridge University Press |
Total Pages |
: 260 |
Release |
: 2000-07-20 |
ISBN-10 |
: 0521789443 |
ISBN-13 |
: 9780521789448 |
Rating |
: 4/5 (43 Downloads) |
Synopsis An Introduction to K-Theory for C*-Algebras by : M. Rørdam
This book provides a very elementary introduction to K-theory for C*-algebras, and is ideal for beginning graduate students.
Author |
: Heath Emerson |
Publisher |
: Springer Nature |
Total Pages |
: 548 |
Release |
: |
ISBN-10 |
: 9783031598500 |
ISBN-13 |
: 3031598504 |
Rating |
: 4/5 (00 Downloads) |
Synopsis An Introduction to C*-Algebras and Noncommutative Geometry by : Heath Emerson
Author |
: Ronald G. Douglas |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 214 |
Release |
: 1982 |
ISBN-10 |
: 9780821850114 |
ISBN-13 |
: 0821850113 |
Rating |
: 4/5 (14 Downloads) |
Synopsis Operator Algebras and $K$-Theory by : Ronald G. Douglas
Author |
: Bruce Blackadar |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 347 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781461395720 |
ISBN-13 |
: 1461395720 |
Rating |
: 4/5 (20 Downloads) |
Synopsis K-Theory for Operator Algebras by : Bruce Blackadar
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.
Author |
: M. Hazewinkel |
Publisher |
: Springer |
Total Pages |
: 927 |
Release |
: 2013-12-01 |
ISBN-10 |
: 9781489937971 |
ISBN-13 |
: 1489937978 |
Rating |
: 4/5 (71 Downloads) |
Synopsis Encyclopaedia of Mathematics by : M. Hazewinkel