K Theory For Operator Algebras
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K Theory For Operator Algebras
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Author : Bruce Blackadar
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
K Theory For Operator Algebras written by Bruce Blackadar 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.
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.
Operator Algebras And Applications Volume 1 Structure Theory K Theory Geometry And Topology
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Author : David E. Evans
language : en
Publisher: Cambridge University Press
Release Date : 1988
Operator Algebras And Applications Volume 1 Structure Theory K Theory Geometry And Topology written by David E. Evans and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
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.
Operator Algebras And K Theory
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Author : Ronald G. Douglas
language : en
Publisher: American Mathematical Soc.
Release Date : 1982
Operator Algebras And K Theory written by Ronald G. Douglas 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 1982 with Mathematics categories.
K Theory And Operator Algebras
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Author : B.B. Morrel
language : en
Publisher: Springer
Release Date : 2006-11-14
K Theory And Operator Algebras written by B.B. Morrel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
K Theory And Operator Algebras
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Author : B. B. Morrel
language : en
Publisher:
Release Date : 2014-01-15
K Theory And Operator Algebras written by B. B. Morrel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
K Theory And Operator Algebras Proceedings
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Author : Bernard B. Morrel
language : en
Publisher:
Release Date : 1977
K Theory And Operator Algebras Proceedings written by Bernard B. Morrel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with categories.
Topological And Bivariant K Theory
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Author : Joachim Cuntz
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-19
Topological And Bivariant K Theory 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 2007-07-19 with Mathematics categories.
Topological K-theory is one of the most important invariants for noncommutative algebras. Bott periodicity, homotopy invariance, and various long exact sequences distinguish it from algebraic K-theory. This book describes a bivariant K-theory for bornological algebras, which provides a vast generalization of topological K-theory. In addition, it details other approaches to bivariant K-theories for operator algebras. The book studies a number of applications, including K-theory of crossed products, the Baum-Connes assembly map, twisted K-theory with some of its applications, and some variants of the Atiyah-Singer Index Theorem.
An Introduction To K Theory For C Algebras
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Author : M. Rørdam
language : en
Publisher: Cambridge University Press
Release Date : 2000-07-20
An Introduction To K Theory For C Algebras written by M. Rørdam and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-07-20 with Mathematics categories.
This book provides a very elementary introduction to K-theory for C*-algebras, and is ideal for beginning graduate students.
K Theory For Real C Algebras And Applications
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Author : Herbert Schröder
language : en
Publisher: Chapman and Hall/CRC
Release Date : 1993-08-23
K Theory For Real C Algebras And Applications written by Herbert Schröder and has been published by Chapman and Hall/CRC this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-08-23 with Mathematics categories.
This Research Note presents the K-theory and KK-theory for real C*-algebras and shows that these can be successfully applied to solve some topological problems which are not accessible to the tools developed in the complex setting alone.
K Theory And Noncommutative Geometry
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Author : Guillermo Cortiñas
language : en
Publisher: European Mathematical Society
Release Date : 2008
K Theory And Noncommutative Geometry written by Guillermo Cortiñas and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with K-theory categories.
Since its inception 50 years ago, K-theory has been a tool for understanding a wide-ranging family of mathematical structures and their invariants: topological spaces, rings, algebraic varieties and operator algebras are the dominant examples. The invariants range from characteristic classes in cohomology, determinants of matrices, Chow groups of varieties, as well as traces and indices of elliptic operators. Thus K-theory is notable for its connections with other branches of mathematics. Noncommutative geometry develops tools which allow one to think of noncommutative algebras in the same footing as commutative ones: as algebras of functions on (noncommutative) spaces. The algebras in question come from problems in various areas of mathematics and mathematical physics; typical examples include algebras of pseudodifferential operators, group algebras, and other algebras arising from quantum field theory. To study noncommutative geometric problems one considers invariants of the relevant noncommutative algebras. These invariants include algebraic and topological K-theory, and also cyclic homology, discovered independently by Alain Connes and Boris Tsygan, which can be regarded both as a noncommutative version of de Rham cohomology and as an additive version of K-theory. There are primary and secondary Chern characters which pass from K-theory to cyclic homology. These characters are relevant both to noncommutative and commutative problems and have applications ranging from index theorems to the detection of singularities of commutative algebraic varieties. The contributions to this volume represent this range of connections between K-theory, noncommmutative geometry, and other branches of mathematics.