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.
The RFD property for graph $C^*$-algebras
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abstract
It is proved that the C*-algebra of a graph is residually finite dimensional (RFD) if and only if the graph has no infinite receiver, no cycle with an exit, no infinite ackward chain and from each vertex, there is a finite path to a sink or a cycle or an 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.