The K-theory of some reduced inverse semigroup C*-algebras
Abstract
We use a recent result by Cuntz, Echterhoff and Li about the K-theory of certain reduced C*-crossed products to describe the K-theory of C*r(S) when S is an inverse semigroup satisfying certain requirements. A result of Milan and Steinberg allows us to show that C*r(S) is Morita equivalent to a crossed product of the type handled by Cuntz, Echterhoff and Li. We apply our result to graph inverse semigroups and the inverse semigroups of one-dimensional tilings.
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