Correspondences between graph C*-algebras
Operator Algebras
2025-06-25 v2
Abstract
We describe proper correspondences from graph C*-algebras to arbitrary C*-algebras by K-theoretic data. If the target C*-algebra is a graph C*-algebra as well, we may lift an isomorphism on a certain invariant to correspondences back and forth that are inverse to each other up to ideal-preserving homotopy. This implies a classification theorem for purely infinite graph C*-algebras up to stable isomorphism.
Keywords
Cite
@article{arxiv.2404.06596,
title = {Correspondences between graph C*-algebras},
author = {Rasmus Bentmann and Ralf Meyer},
journal= {arXiv preprint arXiv:2404.06596},
year = {2025}
}
Comments
30 pages; revision corrected a few typos and some small errors in {\S}9