The KK-theory of amalgamated free products
Operator Algebras
2016-12-28 v3 K-Theory and Homology
Abstract
We prove a long exact sequence in KK-theory for both full and reduced amalgamated free products in the presence of conditional expectations. In the course of the proof, we established the KK-equivalence between the full amalgamated free product of two unital C*-algebras and a newly defined reduced amalgamated free product that is valid even for non GNS-faithful conditional expectations. Our results unify, simplify and generalize all the previous results obtained before by Cuntz, Germain and Thomsen.
Keywords
Cite
@article{arxiv.1510.02418,
title = {The KK-theory of amalgamated free products},
author = {Pierre Fima and Emmanuel Germain},
journal= {arXiv preprint arXiv:1510.02418},
year = {2016}
}
Comments
V.3, the paper has been splitted into two papers, this is the first part on amalgamated free products