Rigidity of twisted groupoid Lp-operator algebras

Abstract

In this paper we study the isomorphism problem for reduced twisted group and groupoid Lp-operator algebras. For a locally compact group G and a continuous 2-cocycle σ we define the reduced σ-twisted Lp-operator algebra Fp λ (G, σ). We show that if p ∈ (1,∞) \ {2}, 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 E over an ´etale groupoid G, we define the reduced twisted groupoid Lpoperator algebra Fp λ (G; E). In the main result of this paper, we show that for p ∈ [1,∞) \ {2} if the groupoids are topologically principal, Hausdorff, étale 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.