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arxiv: 1807.01686 · v1 · pith:CBIH6264new · submitted 2018-07-04 · 🧮 math.OA

C^*-algebras of self-similar graphs over arbitrary graphs

Ruy Exel , Enrique Pardo , Charles Starling This is my paper
classification 🧮 math.OA
keywords casegraphsarbitraryself-similaralgebraalgebrasassociatedcharacterize
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In this note we extend the construction of a $C^*$-algebra associated to a self-similar graph to the case of arbitrary countable graphs. We reduce the problem to the row-finite case with no sources, by using a desingularization process. Finally, we characterize simplicity in this case.

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  1. The ideal structures of self-similar $k$-graph C*-algebras

    math.OA 2019-06 unverdicted novelty 6.0

    Proves a one-to-one correspondence between G-hereditary and G-saturated subsets of vertices and gauge-invariant diagonal-invariant ideals in the C*-algebra of a self-similar k-graph.