Representing Kirchberg algebras as inverse semigroup crossed products

الأصل · EN

In this note we show that a combinatorial model of Kirchberg algebras in the UCT, namely the Katsura algebras OAB, 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 OAB using different methods than those used by Katsura.