Representing Kirchberg algebras as inverse semigroup crossed products

Abstract

In this note we show that a combinatorial model of Kirchberg algebr as in the UCT, namely the Katsura algebras O A,B , can be expressed both as groupoid C ∗ -algebras and as inverse semigroup crossed products. We use this picture to obt ain results about simplicity, pure infiniteness and nuclearity of O A,B using different methods than those used by Katsura.