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.

中文翻译：

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Katsura–Exel–Pardo groupoid的同源性

我们计算了与Katsura代数相关的类群的同源性，并显示出它们在Matui发表的（HK）猜想的意义上捕捉了$ C ^ * $-代数的$ K $理论。此外，我们证明了几个可分类的简单$ C ^ * $-代数是此类的类群$ C ^ * $-代数。