REVIEW 2 cited by
A rigidity framework for Roe-like algebras
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original abstract
In this memoir we develop a framework to study rigidity problems for Roe-like C*-algebras of countably generated coarse spaces. The main goal is to give a complete and self-contained solution to the problem of C*-rigidity for proper (extended) metric spaces. Namely, we show that (stable) isomorphisms among Roe algebras always give rise to coarse equivalences. The material is organized as to provide a unified proof of C*-rigidity for Roe algebras, algebras of operators of controlled propagation, and algebras of quasi-local operators. We also prove a more refined C*-rigidity statement which has several additional applications. For instance, we can put the correspondence between coarse geometry and operator algebras in a categorical framework, and we prove that the outer automorphism groups of these C*-algebras are all isomorphic to the group of coarse equivalences of the coarse space.
Forward citations
Cited by 2 Pith papers
-
Isomorphism rigidity of uniform Roe algebras over arbitrary uniformly locally finite coarse spaces
Isomorphism of uniform Roe algebras over uniformly locally finite coarse spaces forces bijective coarse equivalence of the underlying spaces.
-
C*-rigidity of bounded geometry metric spaces
Uniformly locally finite metric spaces with isomorphic Roe algebras are coarsely equivalent, and the outer automorphism group of the Roe algebra is canonically isomorphic to the group of coarse equivalences.
Discussion (0). Continue with ORCID to comment.