K-Theory and C*-Algebras: A Friendly Approach

Erscheinungsjahr 1993
ISBN: 978-0-19-859694-3
Verlag: Oxford University Press

Buch, Englisch, 382 Seiten, Format (B × H): 161 mm x 241 mm, Gewicht: 760 g

K-theory is often considered a complicated `specialist's' theory. This book is an introduction to the basics and provides detailed explanation of the various concepts required for a deeper understanding of the subject. Some familiarity with basic C*algebra theory is assumed and then follows a careful construction and analysis of the operator K-theory groups and proof of the results of K-theory, including Bott periodicity.

Of specific interest to algebraists and geometrists, the book aims to give full instruction. No details are left out in the presentation and many instructive and generously hinted exercises are provided.

Apart from K-theory, this book offers complete and self contained expositions of important advanced C*-algebraic constructions like tensor products, multiplier algebras and Hilbert modules.

Autoren/Hrsg.

Wegge-Olsen, N. E.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie

Inhaltsverzeichnis

- General notation

- Introduction

- Part I: C*-algebras

- 1: C*-algebras - a summary

- 2: Multiplier algebras

- 3: Extensions of C*-algebras

- 4: Invertibles and unitaries

- 5: Projections

- Part II: Fundamentals of K-Theory

- 6: K0-basic properties

- 7: K1 and suspensions

- 8: The index map in K-theory

- 9: Bott periodicity

- 10: K-theory for multiplier algebras

- 11: Homology

- 12: Some examples: AF-algebras, Cuntz algebras, rotation algebras

- 13: Vector bundles and topological K-theory

- Part III: Hilbert Modules and a Generalized Index Theory

- 14: The classical Fredholm index

- 15: Hilbert modules

- 16: The Kuiper-Mingo theorem

- 17: A generalized Fredholm index

- Part IV: Appendices

- G: The Grothendieck group

- L: Inductive limits

- O: (Dis)order and positivity in C*-algebras

- T: Tensor products -or: the importance of being subcross

- References

- Subject index