nLab K-Theory for Operator Algebras



Operator algebra

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



field theory:

Lagrangian field theory


quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization



States and observables

Operator algebra

Local QFT

Perturbative QFT

Index theory

This entry collects links for the book

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


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 March 14, 2021 at 15:17:25. See the history of this page for a list of all contributions to it.