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lgli/Rordam M., Larsen F., Laustsen N. Introduction to K-theory for C-star-algebras (CUP, 2000)(ISBN 0521783348)(T)(254s)_MCf_.pdf
An Introduction to K-Theory for C*-Algebras (London Mathematical Society Student Texts, Series Number 49) 🔍
M. Rørdam, F. Larsen, N. Laustsen Cambridge University Press (Virtual Publishing), 1st edition, January 15, 2000
英语 [en] · PDF · 8.9MB · 2000 · 📘 非小说类图书 · 🚀/lgli/lgrs · Save
描述
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.
备用文件名
lgrsnf/Rordam M., Larsen F., Laustsen N. Introduction to K-theory for C-star-algebras (CUP, 2000)(ISBN 0521783348)(T)(254s)_MCf_.pdf
备选作者
Rørdam, M., Larsen, F., Laustsen, N.
备选作者
F Larsen; N. J Laustsen; M Rørdam
备用版本
London Mathematical Society student texts, 49, Cambridge, UK, 2000
备用版本
Cambridge University Press, Cambridge, UK, 2000
备用版本
United Kingdom and Ireland, United Kingdom
备用描述
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.
备用描述
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.
备用描述
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
备用描述
This chapter contains some basic facts about C*-algebras that the reader is assumed to be (or become) familiar with.
开源日期
2024-09-28
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