Cartan subalgebras for non-principal twisted groupoid C^⁎-algebras

Authors

Anna L. Duwenig, University of WollongongFollow
E Gillaspy
R Norton
S Reznikoff
S Wright

RIS ID

143123

Publication Details

Duwenig, A., Gillaspy, E., Norton, R., Reznikoff, S. & Wright, S. (2020). Cartan subalgebras for non-principal twisted groupoid C^⁎-algebras. Journal of Functional Analysis, 279 (6),

Abstract

2020 Elsevier Inc. 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.