K Theory For Real C Algebras And Applications
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K Theory for Real C Algebras and Applications
Author | : Herbert Schröder |
Publsiher | : Chapman and Hall/CRC |
Total Pages | : 184 |
Release | : 1993-08-23 |
Genre | : Mathematics |
ISBN | : UOM:39015029969386 |
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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.
An Introduction to K Theory for C Algebras
Author | : M. Rørdam,Flemming Larsen,N. Laustsen |
Publsiher | : Cambridge University Press |
Total Pages | : 260 |
Release | : 2000-07-20 |
Genre | : Mathematics |
ISBN | : 0521789443 |
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This book provides a very elementary introduction to K-theory for C*-algebras, and is ideal for beginning graduate students.
K Theory for Group C Algebras and Semigroup C Algebras
Author | : Joachim Cuntz,Siegfried Echterhoff,Xin Li,Guoliang Yu |
Publsiher | : Birkhäuser |
Total Pages | : 322 |
Release | : 2017-10-24 |
Genre | : Mathematics |
ISBN | : 9783319599151 |
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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.
K theory for Real C algebras and Applications
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Author | : Herbert Schröder |
Publsiher | : Halsted Press |
Total Pages | : 162 |
Release | : 1993 |
Genre | : Algebra |
ISBN | : 0470221690 |
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K Theory for Operator Algebras
Author | : Bruce Blackadar |
Publsiher | : Springer Science & Business Media |
Total Pages | : 347 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9781461395720 |
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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.
Algebraic K theory And Its Applications Proceedings Of The School
Author | : Hyman Bass,Aderemi Oluyomi Kuku,C Pedrini |
Publsiher | : World Scientific |
Total Pages | : 622 |
Release | : 1999-03-12 |
Genre | : Electronic Book |
ISBN | : 9789814544795 |
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The Proceedings volume is divided into two parts. The first part consists of lectures given during the first two weeks devoted to a workshop featuring state-of-the-art expositions on 'Overview of Algebraic K-theory' including various constructions, examples, and illustrations from algebra, number theory, algebraic topology, and algebraic/differential geometry; as well as on more concentrated topics involving connections of K-theory with Galois, etale, cyclic, and motivic (co)homologies; values of zeta functions, and Arithmetics of Chow groups and zero cycles. The second part consists of research papers arising from the symposium lectures in the third week.
Algebraic K Theory and Its Applications
Author | : Jonathan Rosenberg |
Publsiher | : Springer Science & Business Media |
Total Pages | : 404 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9781461243144 |
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Algebraic K-Theory is crucial in many areas of modern mathematics, especially algebraic topology, number theory, algebraic geometry, and operator theory. This text is designed to help graduate students in other areas learn the basics of K-Theory and get a feel for its many applications. Topics include algebraic topology, homological algebra, algebraic number theory, and an introduction to cyclic homology and its interrelationship with K-Theory.
Operator Algebras and Applications Volume 1 Structure Theory K theory Geometry and Topology
Author | : David E. Evans,Masamichi Takesaki |
Publsiher | : Cambridge University Press |
Total Pages | : 257 |
Release | : 1988 |
Genre | : Mathematics |
ISBN | : 9780521368438 |
Download Operator Algebras and Applications Volume 1 Structure Theory K theory Geometry and Topology Book in PDF, Epub and Kindle
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.