We present a uniqueness theorem for the reduced C*-algebra of a twist E over a Hausdorff etale groupoid G. We show that the interior I-E of the isotropy of E is a twist over the interior I-G of the isotropy of G, and that the reduced twisted groupoid C*-algebra C-r* (I-G; I-E) embeds in C-r* (G; E). We also investigate the full and reduced twisted C*-algebras of the isotropy groups of G, and we provide a sufficient condition under which states of (not necessarily unital) C*-algebras have unique state extensions. We use these results to prove our uniqueness theorem, which states that a C*-homomorphism of C-r* (G; E) is injective if and only if its restriction to C-r* (I-G; I-E) is injective. We also show that if G is effective, then C-r* (G; E) is simple if and only if G is minimal. (c) 2022 Elsevier Inc. All rights reserved.
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