JournalsggdVol. 8, No. 2pp. 485–512

On inverse semigroup CC^*-algebras and crossed products

  • David Milan

    The University of Texas at Tyler, USA
  • Benjamin Steinberg

    City College of New York, USA
On inverse semigroup $C^*$-algebras and crossed products cover
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Abstract

We describe the CC^*-algebra of an EE-unitary or strongly 00-EE-unitary inverse semigroup as the partial crossed product of a commutative CC^*-algebra by the maximal group image of the inverse semigroup. We give a similar result for the CC^*-algebra of the tight groupoid of an inverse semigroup. We also study conditions on a groupoid CC^*-algebra to be Morita equivalent to a full crossed product of a commutative CC^*-algebra with an inverse semigroup, generalizing results of Khoshkam and Skandalis for crossed products with groups.

Cite this article

David Milan, Benjamin Steinberg, On inverse semigroup CC^*-algebras and crossed products. Groups Geom. Dyn. 8 (2014), no. 2, pp. 485–512

DOI 10.4171/GGD/236