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Rigidity of twisted groupoid L^p-operator algebras
In this paper we will study the isomorphism problem for the reduced twisted
group and groupoid -operator algebras. For a locally compact group and
a continuous 2-cocycle we will define the reduced -twisted
-operator algebra . We will show that if ,
then two such algebras are isometrically isomorphic if and only if the groups
are topologically isomorphic and the continuous 2-cocyles are cohomologous. For
a twist over an \'etale groupoid , we define the
reduced twisted groupoid -operator algebra
. In the main result of this paper, we
show that for if the groupoids are topologically principal,
Hausdorff, \'etale and have a compact unit space, then two such algebras are
isometrically isomorphic if and only if the groupoids are isomorphic and the
twists are properly isomorphic