374 research outputs found
Characterizing groupoid C*-algebras of non-Hausdorff \'etale groupoids
Given a non-necessarily Hausdorff, topologically free, twisted etale groupoid
, we consider its "essential groupoid C*-algebra", denoted
, obtained by completing with the smallest among
all C*-seminorms coinciding with the uniform norm on . The inclusion
of C*-algebras is then proven to satisfy a list
of properties characterizing it as what we call a "weak Cartan inclusion". We
then prove that every weak Cartan inclusion , with separable, is
modeled by a topologically free, twisted etale groupoid, as above. In another
main result we give a necessary and sufficient condition for an inclusion of
C*-algebras to be modeled by a twisted etale groupoid based on the
notion of "canonical states". A simplicity criterion for is
proven and many examples are provided.Comment: New references and a new main result characterizing arbitrary twisted
etale groupoid C*-algebras were added. The title was changed to account for
the inclusion of the new main result. Still a preliminary versio
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