Decomposable partial actions

Fernando Abadie, Eusebio Gardella, Shirly Geffen

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We define the decomposition property for partial actions of discrete groups on C-algebras. Decomposable partial systems appear naturally in practice, and many commonly occurring partial actions can be decomposed into partial actions with the decomposition property. For instance, any partial action of a finite group is an iterated extension of decomposable systems. Partial actions with the decomposition property are always globalizable and amenable, regardless of the acting group, and their globalization can be explicitly described in terms of certain global sub-systems. A direct computation of their crossed products is also carried out. We show that partial actions with the decomposition property behave in many ways like global actions of finite groups (even when the acting group is infinite), which makes their study particularly accessible. For example, there exists a canonical faithful conditional expectation onto the fixed point algebra, which is moreover a corner in the crossed product in a natural way. (Both of these facts are in general false for partial actions of finite groups.) As an application, we show that freeness of a topological partial action with the decomposition property is equivalent to its fixed point algebra being Morita equivalent to its crossed product. We also show by example that this fails for general partial actions of finite groups.

Original languageEnglish
Article number109112
JournalJournal of Functional Analysis
Issue number7
StatePublished - 1 Oct 2021


  • C-algebras
  • Crossed products
  • Fixed point algebras
  • Partial actions

ASJC Scopus subject areas

  • Analysis


Dive into the research topics of 'Decomposable partial actions'. Together they form a unique fingerprint.

Cite this