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

Abstract

We introduce the Exel-Pardo $\ast$-algebra ${\mathrm{EP}}_R(G,\Lambda )$ associated to a self-similar $k$-graph $(G,\Lambda ,\phi )$. 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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