Renault proved that the reduced C*-algebra of a topologically principal groupoid has a canonical Cartan subalgebra, and that in fact the converse holds: the presence of a Cartan subalgebra guarantees that a C*-algebra has a groupoid model. We examine twisted C*-algebras of non-topologically principal groupoids, identifying conditions on a subgroupoid that suffice to show it will generate a Cartan subalgebra.
This is joint work with Anna Duwenig, Elizabeth Gillaspy, Rachael Norton, and Sarah Wright.
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