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Multiinterval subfactors and modularity of representations in conformal field theory
 Commun. Math. Phys
"... Dedicated to John E. Roberts on the occasion of his sixtieth birthday We describe the structure of the inclusions of factors A(E) ⊂A(E ′ ) ′ associated with multiintervals E ⊂ R for a local irreducible net A of von Neumann algebras on the real line satisfying the split property and Haag duality. I ..."
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Cited by 112 (37 self)
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Dedicated to John E. Roberts on the occasion of his sixtieth birthday We describe the structure of the inclusions of factors A(E) ⊂A(E ′ ) ′ associated with multiintervals E ⊂ R for a local irreducible net A of von Neumann algebras on the real line satisfying the split property and Haag duality. In particular, if the net is conformal and the subfactor has finite index, the inclusion associated with two separated intervals is isomorphic to the LongoRehren inclusion, which provides a quantum double construction of the tensor category of superselection sectors of A. As a consequence, the index of A(E) ⊂A(E ′ ) ′ coincides with the global index associated with all irreducible sectors, the braiding symmetry associated with all sectors is nondegenerate, namely the representations of A form a modular tensor category, and every sector is a direct sum of sectors with finite dimension. The superselection structure is generated by local data. The same results hold true if conformal invariance is replaced by strong additivity and there exists a modular PCT symmetry.
On a simple unital projectionless C∗algebras
 Amer. J. Math
, 1999
"... Abstract. We construct a unital separable Calgebra Z as an analog of the hyperfinite type II1 factor. Besides being nuclear, simple, projectionless, and infinitedimensional, Z has a unique tracial state, and is KKequivalent to C, the algebra of complex numbers. It is shown that unital endomorphis ..."
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Cited by 80 (1 self)
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Abstract. We construct a unital separable Calgebra Z as an analog of the hyperfinite type II1 factor. Besides being nuclear, simple, projectionless, and infinitedimensional, Z has a unique tracial state, and is KKequivalent to C, the algebra of complex numbers. It is shown that unital endomorphisms on Z are approximately inner, and that Z is isomorphic to the infinite tensor product of its replicas. It is also shown that A = Z A for certain interesting classes of unital simple nuclear Calgebras A of real rank zero. 0. Introduction. The goal of this paper is to introduce a simple unital projectionless Calgebra and to take first steps towards an analysis of its structure. The study of projections in Calgebras has long been an important part of their structure theory, and has been particularly fruitful in the last two decades thanks to the advances in Ktheory for Calgebras. In particular, interesting
Hyperlinear and sofic groups: a brief guide
 Bull. Symbolic Logic
"... Relatively recently, two new classes of (discrete, countable) groups have been isolated: hyperlinear groups and sofic groups. They come from different corners of mathematics (operator algebras and symbolic dynamics, respectively), and were introduced independently from each other, but are closely re ..."
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Cited by 67 (1 self)
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Relatively recently, two new classes of (discrete, countable) groups have been isolated: hyperlinear groups and sofic groups. They come from different corners of mathematics (operator algebras and symbolic dynamics, respectively), and were introduced independently from each other, but are closely related nevertheless.
Deformation and rigidity for group actions and von Neumann algebras
, 2007
"... We present some recent rigidity results for von Neumann algebras (II1 factors) and equivalence relations arising from measure preserving actions of groups on probability spaces which satisfy a combination of deformation and rigidity properties. This includes strong rigidity results for factors wit ..."
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Cited by 64 (7 self)
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We present some recent rigidity results for von Neumann algebras (II1 factors) and equivalence relations arising from measure preserving actions of groups on probability spaces which satisfy a combination of deformation and rigidity properties. This includes strong rigidity results for factors with calculation of their fundamental group and cocycle superrigidity for actions with applications to orbit equivalence ergodic theory.
Free products of hyperfinite von Neumann algebras and free dimension
 DUKE MATH. J
, 1992
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On the Ktheory of CuntzKrieger algebras
 Publ. RIMS, Kyoto Univ
, 1996
"... CuntzKrieger algebras of infinite graphs and matrices ..."
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Cited by 47 (17 self)
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CuntzKrieger algebras of infinite graphs and matrices
Strong rigidity of generalized Bernoulli actions and computations of their symmetry groups
, 2006
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On certain free product factors via an extended matrix
"... Abstract. A random matrix model for freeness is extended and used to investigate free products of free group factors with matrix algebras and with the hyperfinite II1–factor. The latter is shown to be isomorphic to a free group factor having one additional generator. Introduction. The finite von Neu ..."
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Cited by 34 (8 self)
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Abstract. A random matrix model for freeness is extended and used to investigate free products of free group factors with matrix algebras and with the hyperfinite II1–factor. The latter is shown to be isomorphic to a free group factor having one additional generator. Introduction. The finite von Neumann algebra L(G) associated to a discrete group G was introduced by Murray and von Neumann [5]. It is the von Neumann algebra generated by the representation of G on l 2 (G) by left translation operators, with faithful trace given by the vector–state for δe. They gave the free group factors L(FK) (where FK is the nonabelian free group on K generators), (2 ≤ K ≤ ∞) as examples of type II1 factors which are not hyperfinite.