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arXiv · 2202.06906

Exel-Pardo algebras of self-similar $k$-graphs

Hossein Larki
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Abstract

We introduce the Exel-Pardo $*$-algebra $\mathrm{EP}_R(G,\Lambda)$ associated to a self-similar $k$-graph $(G,\Lambda,\varphi)$. We prove the $\mathbb{Z}^k$-graded and Cuntz-Krieger uniqueness theorems for such algebras and investigate their ideal structure. In particular, we modify the graded uniqueness theorem for self-similar 1-graphs, and then apply it to present $\mathrm{EP}_R(G,\Lambda)$ as a Steinberg algebra and to study the ideal structure.

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Hossein Larki. 2022-02-14. Exel-Pardo algebras of self-similar $k$-graphs. https://arxiv.org/abs/2202.06906

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