The $K$-Theory of Some Reduced Inverse Semigroup $C^*$-Algebras

• Autores: Magnus Dahler Norling
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 117, Nº 2, 2015, págs. 186-202
• Idioma: inglés
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• Resumen

  • 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.