• Corpus ID: 119584958

A new construction of factors of type ${\rm III_1}$

@article{Houdayer2006ANC,
  title={A new construction of factors of type \$\{\rm III\_1\}\$},
  author={Cyril Houdayer},
  journal={arXiv: Operator Algebras},
  year={2006}
}
  • Cyril Houdayer
  • Published 9 January 2006
  • Mathematics
  • arXiv: Operator Algebras
We give in this paper a new construction of factors of type ${\rm III_1}$. Under certain assumptions, we can, thanks to a result by Popa, give a complete classification for this family of factors. Although these factors are never full, we can nevertheless, in many cases, compute Connes' $\tau$ invariant. We obtain a new example of an uncountable family of pairwise non-isomorphic factors of type ${\rm III_1}$ with the same $\tau$ invariant. 
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References

SHOWING 1-10 OF 16 REFERENCES
On a class of type $II_1$ factors with Betti numbers invariants
We prove that a type II1 factor M can have at most one Cartan subalgebra A satisfying a combination of rigidity and compact approximation properties. We use this result to show that within the class…
Almost periodic states and factors of type III1
On Ozawa's Property for Free Group Factors
We give a new proof of a result of Ozawa showing that if a von Neumann subalgebra $Q$ of a free group factor $L\Bbb F_n, 2\leq n\leq \infty$ has relative commutant diffuse (i.e. without atoms), then…
Some prime factorization results for type II1 factors
We prove several unique prime factorization results for tensor products of type II1 factors coming from groups that can be realized either as subgroups of hyperbolic groups or as discrete subgroups…
Free product von Neumann algebras of type
In this paper we will show that most free products of von Neumann algebras with respect to nontracial states produce type IIIA factors (2 #& O) . In addition, for all such 2, examples can be obtained…
Asymptotically invariant sequences and an action of SL (2,Z) on the 2-sphere
LetG be a countable group which acts non-singularly and ergodically on a Lebesgue space (X, ȑ, μ). A sequence (Bn) in ℒ is calledasymptotically invariant in limn μ (BnΔgBn)=0 for everygεG. In this…
FREE QUASI-FREE STATES
To a real Hilbert space and a one-parameter group of orthogonal transformations we associate a C∗-algebra which admits a free quasi-free state. This construction is a freeprobability analog of the…
Strictly Outer Actions of Groups and Quantum Groups
Abstract An action of a locally compact group or quantum group on a factor is said to be strictly outer when the relative commutant of the factor in the crossed product is trivial. We show that all…
Amenability, Kazhdan's property T, strong ergodicity and invariant means for ergodic group-actions
  • K. Schmidt
  • Mathematics
    Ergodic Theory and Dynamical Systems
  • 1981
Abstract This paper discusses the relations between the following properties o finite measure preserving ergodic actions of a countable group G: strong ergodicity (i.e. the non-existence of almost…
On multiplicity and free absorption for free Araki-Woods factors
We show that Ozawa's recent results on solid von Neumann algebras imply that there are free Araki-Woods factors, which fail to have free absorption. We also show that a free Araki-Woods factors…
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