Regular ideals of graph algebras

Let \(C^*(E)\) be the graph C\(^*\)-algebra of a row-finite graph \(E\). We give a complete description of the vertex sets of the gauge-invariant regular ideals of \(C^*(E)\). It is shown that when \(E\) satisfies Condition (L) the regular ideals \(C^*(E)\) are a class of gauge-invariant ideals whic...

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Bibliographic Details
Published in:arXiv.org 2020-05
Main Authors: Brown, Jonathan H, Fuller, Adam H, Pitts, David R, Reznikoff, Sarah A
Format: Article
Language:English
Subjects:
Invariants
Quotients
Vertex sets
Online Access:Get full text
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Summary:Let \(C^*(E)\) be the graph C\(^*\)-algebra of a row-finite graph \(E\). We give a complete description of the vertex sets of the gauge-invariant regular ideals of \(C^*(E)\). It is shown that when \(E\) satisfies Condition (L) the regular ideals \(C^*(E)\) are a class of gauge-invariant ideals which preserve Condition (L) under quotients. That is, we show that if \(E\) satisfies Condition (L) then a regular ideal \(J \unlhd C^*(E)\) is necessarily gauge-invariant. Further, if \(J \unlhd C^*(E)\) is a regular ideal, it is shown that \(C^*(E)/J \simeq C^*(F)\) where \(F\) satisfies Condition (L).
ISSN:2331-8422
DOI:10.48550/arxiv.2006.00395