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

Abstract

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
Volume279
Issue number6
DOIs
StatePublished - Oct 1 2020

Keywords

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

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