Titlebook: Operator Algebras and Dynamics: Groupoids, Crossed Products, and Rokhlin Dimension; Aidan Sims,Gábor Szabó,Dana Williams,Francesc Pere Tex

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Cartan Pairs, and Dixmier–Douady Theory for Fell AlgebrasIn this chapter we first discuss the beautiful reconstruction theorem of Renault [39] that shows that an effective groupoid and twist can be recovered from the associated twisted groupoid algebra.

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Classical Dynamical SystemsIn this part, we will treat the classical Rokhlin lemma. For its generalizations and importance within ergodic theory, the interested reader may consult the excellent recent book of Kerr{Li [27].

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Rokhlin Dimension for Finite GroupsIn order to capture the main idea for the relevance of Rokhlin-type properties to nuclear dimension, it is useful to step back from the single automorphism case and focus first on finite groups. (Note that everything in this section can be generalized to compact groups [20, 14, 13].)

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https://doi.org/10.1007/978-3-030-39713-5crossed products; topological groupoid, groupoid C*-algebra; amenability; Rokhlin dimension; nuclear dim

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Netherlands Yearbook of International Lawhttp://image.papertrans.cn/n/image/662747.jpg