On a groupoid construction for actions of certain inverse semigroups

Details On a groupoid construction for actions of certain inverse semigroups On a groupoid construction for actions of certain inverse semigroups

1993-05-11

arxiv.org/abs/funct-an/9305001v1

Mathematics

Operator Algebras

27 pages, LATEX

Scientific paper

We consider a version of the notion of F-inverse semigroup (studied in the algebraic theory of inverse semigroups). We point out that an action of such an inverse semigroup on a locally compact space has associated a natural groupoid construction, very similar to the one of a transformation group. We discuss examples related to Toeplitz algebras on subsemigroups of discrete groups,to Cuntz-Krieger algebras, and to crossed-products by partial automorphisms in the sense of Exel.

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