Do phantom Cuntz-Krieger algebras exist?
Sara Arklint
TL;DR
This paper surveys the current knowledge on whether phantom Cuntz-Krieger algebras exist, exploring their potential non-existence and implications for characterizing real rank zero Cuntz-Krieger algebras.
Contribution
It provides a comprehensive summary of known results regarding the non-existence of phantom Cuntz-Krieger algebras and their impact on algebra classification.
Findings
Phantom Cuntz-Krieger algebras likely do not exist
Real rank zero Cuntz-Krieger algebras can be characterized by outer properties if no phantom algebras exist
The paper consolidates existing results and open questions in this area
Abstract
If phantom Cuntz-Krieger algebras do not exist, then real rank zero Cuntz-Krieger algebras can be characterized by outer properties. In this survey paper, a summary of the known results on non-existence of phantom Cuntz-Krieger algebras is given.
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Taxonomy
TopicsAdvanced Algebra and Logic · Advanced Topics in Algebra · Advanced Operator Algebra Research