REVIEW 2 cited by
On Kumjian's C*-diagonals and the opaque ideal
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
abstract
We characterize exotic C*-algebras of twisted, principal \'etale groupoids, together with the abelian subalgebra associated to the unit space, as precisely being the inclusions "$A\subseteq B$" of C*-algebras in which $A$ is abelian, regular, and satisfies the extension property (pure states extend uniquely to $B$). When $B$ is moreover nuclear, we deduce that the corresponding opaque ideal is trivial. As an application, we give a streamlined characterization of Kumjian's C*-diagonals as the regular abelian subalgebras satisfying the extension property with vanishing opaque ideal.
Forward citations
Cited by 2 Pith papers
-
A C*-diagonal in the Jiang-Su algebra via entangled matrix cones
An explicit inductive system of entangled dimension-drop algebras realises Z and yields a C*-diagonal with one-dimensional non-locally-connected spectrum, via a new normaliser characterisation by state excision.
-
Pseudo-Cartan Inclusions
For regular inclusions with abelian subalgebra, having a Cartan envelope is equivalent to having a faithful unique pseudo-expectation, now proven without the unital hypothesis.
Discussion (0). Continue with ORCID to comment.