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• W2154528415 abstract "We give sufficient conditions, in terms of the existence of unbounded derivations satisfying certain properties, which ensure that a II$_1$ factor $M$ is prime or has at most one Cartan subalgebra. For instance, we prove that if there exists a real closable unbounded densely defined derivation $delta:Mrightarrow L^2(M)bar{otimes}L^2(M)$ whose domain contains a non-amenability set, then $M$ is prime. If $delta$ is moreover algebraic (i.e. its domain $M_0$ is finitely generated, $delta(M_0)subset M_0otimes M_0$ and $delta^*(1otimes 1)in M_0$), then we show that $M$ has no Cartan subalgebra. We also give several applications to examples from free probability. Finally, we provide a class of countable groups $Gamma$, defined through the existence of an unbounded cocycle $b:Gammarightarrow mathbb C(Gamma/Lambda)$, for some subgroup $Lambda<Gamma$, such that the II$_1$ factor $L^{infty}(X)rtimesGamma$ has a unique Cartan subalgebra, up to unitary conjugacy, for any free ergodic probability measure preserving (pmp) action $Gammacurvearrowright (X,mu)$." @default.
• W2154528415 created "2016-06-24" @default.
• W2154528415 creator A5052788604 @default.
• W2154528415 creator A5070665706 @default.
• W2154528415 date "2012-12-27" @default.
• W2154528415 modified "2023-09-27" @default.
• W2154528415 title "Unbounded derivations, free dilations and indecomposability results for II$_1$ factors" @default.
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• W2154528415 hasPublicationYear "2012" @default.
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