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

Abstract

We introduce the Exel-Pardo * -algebra EPR(G, Λ) associated to a self-similar kgraph (G, Λ, ϕ). We prove the 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 EPR(G, Λ) as a Steinberg algebra and to study the ideal structure.