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K-Theory and C*-Algebras : A Friendly Approach - N. E. Wegge-Olsen

K-Theory and C*-Algebras

A Friendly Approach


Published: 11th March 1993
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K-theory is often considered a complicated mathematical theory for specialists only. This book is an accessible introduction to the basics and provides detailed explanations of the various concepts required for a deeper understanding of the subject. Some familiarity with basic C*algebra theory is assumed. The book 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.

'no details are left out in the presentation, and many instructive and generously hinted exercises are provided' L'Enseignement Mathématique, 3-4 1993 `... it is written in a very lively and user friendly style... Altogether I think this book is very recommendable as a first introduction to the subject.' Monatshefte fur Mathematik, 3 April 1995

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

ISBN: 9780198596943
ISBN-10: 0198596944
Series: Oxford Science Publications
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 382
Published: 11th March 1993
Publisher: Oxford University Press
Country of Publication: GB
Dimensions (cm): 24.1 x 16.1  x 2.6
Weight (kg): 0.77