An Introduction to K-Theory for C*-Algebras (London Mathematical Society Student Texts, Series Number 49)

Over the past twenty-five years K-theory has become an integrated part of the study of C*-algebras. This book gives a very elementary introduction to this interesting and rapidly growing area of mathematics. The authors cover the basic properties of the functors K and K1 and their interrelationship. In particular, the Bott periodicity theorem is proved (Atiyah's proof), and the six-term exact sequence is derived. The theory is well illustrated with 120 exercises and examples, making the book ideal for beginning graduate students in functional analysis, especially operator algebras, and for researchers from other areas of mathematics who want to learn about this subject. Over The Last 25 Years K-theory Has Become An Integrated Part Of The Study Of C*-algebras. This Book Gives An Elementary Introduction To This Interesting And Rapidly Growing Area Of Mathematics. Fundamental To K-theory Is The Association Of A Pair Of Abelian Groups, K0(a) And K1(a), To Each C*-algebra A. These Groups Reflect The Properties Of A In Many Ways. This Book Covers The Basic Properties Of The Functors K0 And K1 And Their Interrelationship. Applications Of The Theory Include Elliott's Classification Theorem For Af-algebras, And It Is Shown That Each Pair Of Countable Abelian Groups Arises As The K-groups Of Some C*-algebra.--pub. Desc. 1. C*-algebra Theory -- 2. Projections And Unitary Elements -- 3. The K0-group Of A Unital C*-algebra -- 4. The Functor K0 -- 5. The Ordered Abelian Group K0(a) -- 6. Inductive Limit C*-algebras -- 7. Classification Of Af-algebras -- 8. The Functor K1 -- 9. The Index Map -- 10. The Higher K-functors -- 11. Bott Periodicity -- 12. The Six-term Exact Sequence -- 13. Inductive Limits Of Dimension Drop Algebras. M. Rørdam, F. Larsen, N. Laustsen. Includes Bibliographical References (p.231-233) And Indexes. Over the last 25 years K-theory has become an integrated part of the study of C•-algebras. This book gives an elementary introduction to this interesting and rapidly growing area of mathematics. Fundamental to K-theory is the association of a pair of Abelian groups, K0(A) and K1(A), to each C•-algebra A. These groups reflect the properties of A in many ways. This book covers the basic properties of the functors K0 and K1 and their interrelationship. Applications of the theory include Elliott's classification theorem for AF-algebras, and it is shown that each pair of countable Abelian groups arises as the K-groups of some C•-algebra. The theory is well illustrated with 120 exercises and examples, making the book ideal for beginning graduate students working in functional analysis, especially operator algebras, and for researchers from other areas of mathematics who want to learn about this subject. Frontmatter Contents Preface Chapter 1 C*-Algebra Theory Chapter 2 Projections and Unitary Elements Chapter 3 The K_0-Group of a Unital C*-Algebra Chapter 4 The Functor K_0 Chapter 5 The Ordered Abelian Group K_0(A) Chapter 6 Inductive Limit C*-Algebras Chapter 7 Classification of AF-Algebras Chapter 8 The Functor K_1 Chapter 9 The Index Map Chapter 10 The Higher K-Functors Chapter 11 Bott Periodicity Chapter 12 The Six-Term Exact Sequence Chapter 13 Inductive Limits of Dimension Drop Algebras References Table of K-groups Index of symbols General index This chapter contains some basic facts about C*-algebras that the reader is assumed to be (or become) familiar with.