Regular ideals of graph algebras
Jonathan H. Brown, Adam H. Fuller, David R. Pitts, Sarah A. Reznikoff

TL;DR
This paper characterizes the structure of regular ideals in graph C*-algebras, showing how they relate to gauge-invariance and preserving Condition (L) in quotients, with a complete description of their vertex sets.
Contribution
It provides a full description of gauge-invariant regular ideals in graph C*-algebras and demonstrates their stability under quotients when Condition (L) is satisfied.
Findings
Regular ideals are gauge-invariant under Condition (L).
Quotients by regular ideals preserve Condition (L).
Vertex sets of regular ideals are fully characterized.
Abstract
Let be the graph C-algebra of a row-finite graph . We give a complete description of the vertex sets of the gauge-invariant regular ideals of . It is shown that when satisfies Condition (L) the regular ideals are a class of gauge-invariant ideals which preserve Condition (L) under quotients. That is, we show that if satisfies Condition (L) then a regular ideal is necessarily gauge-invariant. Further, if is a regular ideal, it is shown that where satisfies Condition (L).
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
