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Homology of the Katsura-Exel-Pardo groupoid (1806.09297v3)

Published 25 Jun 2018 in math.OA

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, and hence satisfying the (HK) conjecture posted by Matui. Moreover, we show that several classifiable simple $C^*$-algebras are groupoid $C^*$-algebras of this class.