The K-Theory of Some Reduced Inverse Semigroup C^*-Algebras - Norling, Magnus Dahler (Mathematica Scandinavica, 2015)
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.