Tristan Bice, Lisa Orloff Clark, Ying-Fen Lin, Kathryn McCormick
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Cartan semigroups and twisted groupoid C*-algebras
We prove that twisted groupoid C*-algebras are characterised, up to
isomorphism, by having Cartan semigroups, a natural generalisation of
normaliser semigroups of Cartan subalgebras. This extends the classic
Kumjian-Renault theory to general twisted \'etale groupoid C*-algebras, even
non-reduced C*-algebras of non-effective groupoids.
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