2023/09/12 by Jonathan H. Brown, Brown, Jonathan H., Elizabeth Gillaspy +1
Mathematics · #Advanced Operator Algebra Research #Homotopy and Cohomology in Algebraic Topology #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.2309.06539
This paper explores the tension between multiple models and rigidity for groupoid C^*-algebras. We begin by identifying Γ-Cartan subalgebras D inside twisted groupoid C^*-algebras C^*r(G, ω), using similar techniques to those developed in [DGN+20]. When D \not= C0(G(0)), [BFPR21, Theorem 4.19] then gives another groupoid H, and a twist Σ over H, so that D ≅ C0(H(0)) and C^*r(G, ω) ≅ C^*r(H; Σ). However, there is a close relationship between G and H. In addition to showing how to construct H and Σ in terms of G and ω, we also show how to reconstruct G from H if we assume the 2-cocycle ω is trivial. This latter construction involves a new type of twisting datum, which may be of independent interest.