Rigidity of twisted groupoid L^p-operator algebras

2022/09/23 by Hetland, Einar V., Ortega, Eduard · 1 citation
#22D20 #43A15 #47B01 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2209.11447

Abstract

In this paper we will study the isomorphism problem for the reduced twisted group and groupoid L^p-operator algebras. For a locally compact group G and a continuous 2-cocycle σ we will define the reduced σ-twisted L^p-operator algebra F_λ^p(G,σ). We will show that if p≠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 L^p-operator algebra F^p_λ(G;E). In the main result of this paper, we show that for p≠ 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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