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.
$C^*$-algebras of self-similar graphs over arbitrary graphs
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abstract
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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math.OA 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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The ideal structures of self-similar $k$-graph C*-algebras
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.