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arXiv · 2006.00395

Regular ideals of graph algebras

Jonathan H. Brown·Adam H. Fuller·David R. Pitts·Sarah A. Reznikoff
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Abstract

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).

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BibTeXRIS

Jonathan H. Brown, Adam H. Fuller, David R. Pitts, Sarah A. Reznikoff. 2020-05-31. Regular ideals of graph algebras. https://doi.org/10.1216/rmj.2022.52.43

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