Cartan subalgebras for non-principal twisted groupoid C-algebras

A. Duwenig, E. Gillaspy, R. Norton, S. Reznikoff, S. Wright

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Renault proved in 2008 [22, Theorem 5.2] that if G is a topologically principal groupoid, then C0(G(0)) is a Cartan subalgebra in Cr (G,Σ) for any twist Σ over G. However, there are many groupoids which are not topologically principal, yet their (twisted) C-algebras admit Cartan subalgebras. This paper gives a dynamical description of a class of such Cartan subalgebras, by identifying conditions on a 2-cocycle c on G and a subgroupoid S⊆G under which Cr (S,c) is Cartan in Cr (G,c). When G is a discrete group, we also describe the Weyl groupoid and twist associated to these Cartan pairs, under mild additional hypotheses.

Original languageEnglish
Article number108611
JournalJournal of Functional Analysis
Issue number6
StatePublished - Oct 1 2020


  • Cartan subalgebra
  • Groupoid 2-cocycle
  • Twisted groupoid C*-algebra
  • Weyl groupoid


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