Amenability and exactness for dynamical systems and their C*-algebras

By C. Anantharaman-Delaroche. 2000

171 citations recorded by the source corpus.

We study the relations between amenability (resp. amenability at infinity) of C*-dynamical systems and equality or nuclearity (resp. exactness) of the corresponding crossed products.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/564a91ea683a324d423e5420f126fd736d07c0d2

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

The Novikov Conjecture for Linear Groups (2005, background): “For a fuller treatment of the topic the reader is referred to [2] or [31].”
Constructions preserving Hilbert space uniform embeddability of discrete groups (2003, background): “embeddability and exactness are found in the work of Guentner-Kaminker [13]; these preliminary steps were quickly expanded by Ozawa [16], Anantharaman-Delaroche [2] and others.”
Crossed Products of the Cantor Set by Free Minimal Actions of ℤd (2002, background): “Remark 2.17. If the almost AF Cantor groupoid G is a transformation group groupoid � × X (as in Example 1.3), then the answer is yes; in fact, the group � is necessarily amenable. See Example 2.7(3) of [ 1 ].”
Expanders, exact crossed products, and the Baum–Connes conjecture (2013, unknown): “⊙’ denote the algebraic tensor product (over C) between two ∗-algebras, and as usual use ‘⊗’ for the spatial tensor product of C∗-algebras. Recall that we denote elements of A⋊alg Gby (ag)g∈G. Equip C[0,1] with the trivial G-action, and consider the function deﬁned by (4.3) φ: C[0,1]⊙ (A⋊alg G) → (C”
Nilpotent Group C*-algebras as Compact Quantum Metric Spaces (2002, methodology): “14(2) of [3], [2], [26], [25]) there is a sequence”