5,034 research outputs found
Simplicity of algebras associated to \'etale groupoids
We prove that the C*-algebra of a second-countable, \'etale, amenable
groupoid is simple if and only if the groupoid is topologically principal and
minimal. We also show that if G has totally disconnected unit space, then the
associated complex *-algebra introduced by Steinberg is simple if and only if
the interior of the isotropy subgroupoid of G is equal to the unit space and G
is minimal.Comment: The introduction has been updated and minor changes have been made
throughout. To appear in Semigroup Foru
Nontraditional models of -Cartan pairs
This paper explores the tension between multiple models and rigidity for
groupoid -algebras. We begin by identifying -Cartan subalgebras
inside twisted groupoid -algebras , using similar
techniques to those developed in [DGN20]. When ,
[BFPR21, Theorem 4.19] then gives another groupoid , and a twist
over , so that and . However, there is a close relationship between and . In
addition to showing how to construct and in terms of and
, we also show how to reconstruct from if we assume the
2-cocycle is trivial. This latter construction involves a new type of
twisting datum, which may be of independent interest
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