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

NOTE EDITORE

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.

SOMMARIO

1 - C*-algebras - a summary2 - Multiplier algebras3 - Extensions of C*-algebras4 - Invertibles and unitaries5 - Projections6 - K0-basic properties7 - K1 and suspensions8 - The index map in K-theory9 - Bott periodicity10 - K-theory for multiplier algebras11 - Homology12 - Some examples: AF-algebras, Cuntz algebras, rotation algebras13 - Vector bundles and topological K-theory14 - The classical Fredholm index15 - Hilbert modules16 - The Kuiper-Mingo theorem17 - A generalized Fredholm indexG - The Grothendieck groupL - Inductive limitsO - (Dis)order and positivity in C*-algebrasT - Tensor products -or: the importance of being subcross

ALTRE INFORMAZIONI

• Condizione: Nuovo
• ISBN: 9780198596943
• Dimensioni: 241 x 26.0 x 161 mm Ø 760 gr
• Formato: Copertina rigida
• Illustration Notes: line drawings, diagrams
• Pagine Arabe: 382