An introduction to K-theory for C*-algebras

Author(s)

• Rørdam, M
• Larsen, F
• Laustsen, N

Bibliographic Information

An introduction to K-theory for C*-algebras

M. Rørdam, F. Larsen, N. Laustsen

（London Mathematical Society student texts, 49）

Cambridge University Press, 2000

• : hbk
• : pbk

Note

Bibliography: p. [231]-233

Includes indexes

Description and Table of Contents

Description

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.

Table of Contents

• Preface
• 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
• References
• Table of K-groups
• Index of symbols
• General index.

by "Nielsen BookData"

Details

• NCID: BA47393931
• ISBN:
  • 0521783348
  • 0521789443
• Country Code: uk
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Cambridge, UK ; New York, NY
• Pages/Volumes: xii, 242 p.
• Size: 24 cm
• Classification:
  • LCC : QA612.33.R66
  • DC21 : 512.55
• Subject Headings:
  • LCSH : C*-algebras
  • LCSH : K-theory
• Parent Bibliography ID:
  • BA00194352