The KK-Theory of Fundamental C*-Algebras
Operator Algebras
2016-12-28 v1 K-Theory and Homology
Abstract
Given a graph of C*-algebras, we prove a long exact sequence in KK-theory for both the maximal and the vertex-reduced fundamental C*-algebras in the presence of possibly non GNS-faithful conditional expectations. We deduce from it the KK-equivalence between the full fundamental C*-algebra and the vertex-reduced fundamental C*-algebra even for non GNS-faithful conditional expectations. Our results unify, simplify and generalize all the previous results obtained before by Cuntz, Pimsner, Germain and Thomsen. It also generalizes the previous results of the authors on amalgamated free products.
Keywords
Cite
@article{arxiv.1612.08558,
title = {The KK-Theory of Fundamental C*-Algebras},
author = {Fima Pierre and Germain Emmanuel},
journal= {arXiv preprint arXiv:1612.08558},
year = {2016}
}
Comments
V1, 27p: the paper arXiv:1510.02418 has been splitted into two papers. It is the second part on fundamental C*-algebras