The homology of the Katsura-Exel-Pardo groupoid

Abstract

We compute the homology of the groupoid associated to the Katsura algebras, and show that they capture the K-theory of the C ∗ -algebras in the sense of the (HK) conjecture posted by Matui. Moreover, we show that several classifiable simple C ∗ -algebras are groupoid C ∗ -algebras of this class.