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K-Theory for Operator Algebras

Contents

Context

Operator algebra

algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)

Introduction

Concepts

field theory:

Lagrangian field theory

quantization

quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization

renormalization

Theorems

States and observables

Operator algebra

Local QFT

Perturbative QFT

Index theory

This entry collects links for the book

  • Bruce Blackadar,

    K-Theory for Operator Algebras

    Cambridge University Press 1986, second ed. 1999

    (pdf)

on operator algebra, operator K-theory and KK-theory.

Contents

Chapter I. Introduction to K-theory

1. Survey of topological K-theory

2. Overview of operator K-theory

Chapter II. Preliminaries

3. Local Banach algebras and inductive limits

4. Idempotents and Equivalence

Chapter III. K 0K_0-theory and order

5. Basic K 0K_0-theory

(…)

6. Order structure on K 0K_0

(…)

7. Theore of AF algebras

(…)

Chapter IV. K 1K_1-theory and Bott periodicity

8. Higher K-groups

(…)

9. Bott periodictiy

Chapter V. KK-theory of crossed products

10. The Pimsner-Voiculescu exact sequence and Connes’ Thom isomorphism

11. Equivariant K-theory

Chapter VI. More preliminaries

12. Multiplier algebras

13. Hilbert modules

14. Graded C *C^\ast-algebra

Chapter VII. Theory of extensions

15. Basic theory of extensions

(…)

16. Brown-Douglas-Fillmore theory and other applications

(…)

Chapter VIII. KK-theory

17. Basic theory

18. The intersection product

(…)

19. Further structure in KK-theory

(…)

20. Equivariant KK-theory

Chapter IX. Further topics

21. Homology and Cohomology Theories on C *C^\ast-algebras

(…)

22. Axiomatic K-theory

23. Universal coefficient theorems and Künneth theorems

24. Survey of applications to geometry and topology

(…)

25. E-theory

category: reference

Last revised on July 22, 2018 at 15:38:18. See the history of this page for a list of all contributions to it.