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dc.contributor.authorGardella, Eusebio
dc.contributor.authorLupini, Martino
dc.date.accessioned2017-05-04T09:22:23Z
dc.date.available2017-05-04T09:22:23Z
dc.date.issued2017-01-17
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1280
dc.identifier.urihttps://arxiv.org/abs/1612.08217
dc.description2000 Mathematics Subject Classification. Primary 46L55, 54H05; Secondary 03E15, 37A55en_US
dc.descriptionOWLF 2016en_US
dc.description.abstractLet $\Lambda $ be a countably infinite property (T) group, and let $D$ be UHF-algebra of infinite type. We prove that there exists a continuum of pairwise non (weakly) cocycle conjugate, strongly outer actions of $\Lambda $ on $D$. The proof consists in assigning, to any second countable abelian pro-$p$ group $G$, a strongly outer action of $\Lambda $ on $D$ whose (weak) cocycle conjugacy class completely remembers the group $G$. The group $G$ is reconstructed from the action via its (weak) 1-cohomology set endowed with a canonical pairing function. The key ingredient in this computation is Popa's cocycle superrigidity theorem for Bernoulli shifts on the hyperfinite II$_{1} $ factor $R$. Our construction also shows the following stronger statement: the relations of conjugacy, cocycle conjugacy, and weak cocycle conjugacy of strongly outer actions of $\Lambda $ on $D$ are complete analytic sets, and in particular not Borel. The same conclusions hold more generally when $\Lambda $ is only assumed to contain an infinite subgroup with relative property (T), and for actions on (not necessarily simple) separable, nuclear, UHF-absorbing, self-absorbing C*-algebras with at least one trace. Finally, we use the techniques of this paper to construct outer actions on $R$ with prescribed cohomology. Precisely, for every infinite property (T) group $\Lambda$, and for every countable abelian group $\Gamma$, we construct an outer action of $\Lambda$ on $R$ whose 1-cohomology is isomorphic to $\Gamma$.en_US
dc.language.isoenen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2017,01
dc.titleCocycle Superrigidity and Group Actions on Stably Finite C*-Algebrasen_US
dc.typePreprinten_US
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWP-2017-01
local.scientificprogramOWLF 2016en_US
local.series.idOWP-2017-01
local.subject.msc46
local.subject.msc54
local.subject.msc03
local.subject.msc37
dc.identifier.urnurn:nbn:de:101:1-201703313677
dc.identifier.ppn1658007301


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