Exel-Pardo Algebras of Self-Similar k-Graphs

Abstract

We introduce the Exel-Pardo $$*$$ -algebra $${\textrm{EP}}_R(G,\Lambda )$$ associated to a self-similar k-graph $$(G,\Lambda ,\varphi )$$ . We also 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 $${\textrm{EP}}_R(G,\Lambda )$$ as a Steinberg algebra and to study the ideal structure.