Representing Kirchberg algebras as inverse semigroup crossed products

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2013-04-23Department
MatemáticasAbstract
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.
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