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 Fλp(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 étale groupoid G, we define the reduced twisted groupoid Lp-operator algebra Fλp(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.

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