Inverse semigroup expansions and their actions on C*-algebras

Details Inverse semigroup expansions and their actions on C*-algebras Inverse semigroup expansions and their actions on C*-algebras

2011-12-04

arxiv.org/abs/1112.0771v1

Mathematics

Operator Algebras

22 pages

Scientific paper

In this work we give a presentation of the prefix expansion Pr(G) of an inverse semigroup G as recently introduced by Lawson, Margolis and Steinberg which is similar to the universal inverse semigroup defined by the second named author in case G is a group. The inverse semigroup Pr(G) classifies the partial actions of G on spaces. We extend this result and prove that Fell bundles over G correspond bijectively to saturated Fell bundles over Pr(G). In particular, this shows that twisted partial actions of G (on C*-algebras) correspond to twisted (global) actions of Pr(G). Furthermore, we show that this correspondence preserves C*-algebras crossed products.

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