Every self-similar k-graph C*-algebra, for finitely aligned k-graphs, is the tight C*-algebra of an explicitly constructed inverse semigroup, and simplicity can be read off from graphical conditions.
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An inverse semigroup approach to self-similar k-graph $C^*$-algebras and simplicity
Every self-similar k-graph C*-algebra, for finitely aligned k-graphs, is the tight C*-algebra of an explicitly constructed inverse semigroup, and simplicity can be read off from graphical conditions.