Envelope Algebras of Partial Actions as Groupoid C*-Algebras

Details Envelope Algebras of Partial Actions as Groupoid C*-Algebras Envelope Algebras of Partial Actions as Groupoid C*-Algebras

2008-06-19

arxiv.org/abs/0806.3262v1

Mathematics

Operator Algebras

13 pages

Scientific paper

We describe the envelope C*-algebra associated to a partial action of a countable discrete group on a locally compact space as a groupoid C*-algebra (more precisely as a C*-algebra from an equivalence relation) and we use our approach to show that, for a large class of partial actions of Z on the Cantor set, the envelope C*-algebra is an AF-algebra. We also completely characterize partial actions of a countable discrete group on a compact space such that the envelope action acts in a Hausdorff space.

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