Representing Kirchberg algebras as inverse semigroup crossed products

Abstract

In this note we show that a combinatorial model of Kirchberg algebras in the UCT, namely the Katsura algebras O_{AB}, can be expressed both as groupoid C*-algebras and as inverse semigroup crossed products. We use this picture to obtain results about simplicity, pure infiniteness and nuclearity of O_{AB} using different methods than those used by Katsura.

In order to fix an error in Proposition 7.18, Section 7 has been rewritten from Lemma 7.12 onwards. Minor changes in sections 6 and 9. The main results of the paper have not been affected by these changes