An inverse semigroup approach to self-similar k-graph $C^*$-algebras and simplicity

Hossein Larki

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arXiv · 2411.14027

An inverse semigroup approach to self-similar k-graph $C^*$-algebras and simplicity

Hossein Larki

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Abstract

We generalize the Li-Yang notion of self-similar $k$-graph $(G,\Lambda)$ and its $C^*$-algebra $\mathcal{O}_{G,\Lambda}$ to any finitely aligned $k$-graph $\Lambda$. We then introduce an inverse semigroup model for $\mathcal{O}_{G,\Lambda}$ and analyze its tight groupoid and $C^*$-algebra via inverse semigroup methods.

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Hossein Larki. 2024-11-21. An inverse semigroup approach to self-similar k-graph $C^*$-algebras and simplicity. https://arxiv.org/abs/2411.14027

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