A graph C*-algebra is residually finite dimensional if and only if the graph has no infinite receiver, no cycle with an exit, no infinite backward chain, and every vertex reaches a sink, cycle, or infinite emitter.
Decomposition theorems for unital graphC∗-algebras
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We prove that unital graph C*-algebras often admit a convenient decomposition into amalgamated free products. We use this to give a complete characterization of when a unital graph C*-algebra is residually finite-dimensional and when it is operator norm stable (that is, matricially semiprojective).
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math.OA 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Graph-theoretic RFD conditions on ultragraphs imply RFD for their Leavitt path algebras and C*-algebras, with equivalences under RFUM2 via branching systems and groupoid models.
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The RFD property for graph $C^*$-algebras
A graph C*-algebra is residually finite dimensional if and only if the graph has no infinite receiver, no cycle with an exit, no infinite backward chain, and every vertex reaches a sink, cycle, or infinite emitter.
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Residual finite-dimensionality of ultragraph algebras via branching systems
Graph-theoretic RFD conditions on ultragraphs imply RFD for their Leavitt path algebras and C*-algebras, with equivalences under RFUM2 via branching systems and groupoid models.