English

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