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Aperiodicity, topological freeness and more: from group actions to Fell bundles | | B. K. Kwasniewski
; R. Meyer
; | | Date: |
21 Nov 2016 | | Abstract: | We collect and improve many known results that relate conditions for actions
of a discrete group on a $C^*$-algebra $A$ that are sufficient or necessary for
the reduced crossed product to be simple or for $A$ to detect or separate
ideals in it. This concerns notions such as aperiodicity, topologicial
freeness, pure outerness or the Connes spectrum. We extend this theory to Fell
bundles over discrete groups and, in particular, to single Hilbert bimodules.
We also analyse conditions that help to show that reduced cross-sectional
$C^*$-algebras of Fell bundles are purely infinite or strongly purely infinite. | | Source: | arXiv, 1611.6954 | | Services: | Forum | Review | PDF | Favorites | |
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