An axiomatization of the lattice of higher relative commutants of a subfactor.
An example of an irreducible subfactor of the hyperfinite II1 factor with rational, noninteger index.
Classification of subfactors: the reduction to commuting squares.
Commutators associated to a subfactor and its relative commutants
Let be an inclusion of factors with finite Jones index. Then as a vector space. Here denotes the vector space spanned by the commutators of the form where .
Composition of subfactors : new examples of infinite depth subfactors
Crosssed products in bimodules.
Entropy for a pair of subalgebras via automorphisms.
Fusion en algèbres de von Neumann et groupes de lacets
Invariant subspaces for operators in a general II1-factor
Let ℳ be a von Neumann factor of type II1 with a normalized trace τ. In 1983 L. G. Brown showed that to every operator T∈ℳ one can in a natural way associate a spectral distribution measure μ T (now called the Brown measure of T), which is a probability measure in ℂ with support in the spectrum σ(T) of T. In this paper it is shown that for every T∈ℳ and every Borel set B in ℂ, there is a unique closed T-invariant subspace affiliated with ℳ, such that the Brown measure of is concentrated on B...
Irreducible subfactors from some symmetric graphs.
On some convex stes and their exteme points.
On the type III principal graphs of subfactors.
Quantum permutation groups: a survey
This is a presentation of recent work on quantum permutation groups. Contains: a short introduction to operator algebras and Hopf algebras; quantum permutation groups, and their basic properties; diagrams, integration formulae, asymptotic laws, matrix models; the hyperoctahedral quantum group, free wreath products, quantum automorphism groups of finite graphs, graphs having no quantum symmetry; complex Hadamard matrices, cocycle twists of the symmetric group, quantum groups acting on 4 points; remarks...
Random matrices, amalgamated free products and subfactors of the von Neumann algebra of a free group, of noninteger index.
Saturated Actions of Finite Dimensional Hopf *-Algebras on C*-Algebras.
Some properties of the symmetric enveloping algebra of a subfactor, with applications to amenability and property .
The canonical endomorphism for infinite index inclusions.
The relative Dixmier property for inclusions of von Neumann algebras of finite index
Truncation and Duality Results for Hopf Image Algebras
Associated to an Hadamard matrix is the spectral measure μ ∈ [0,N] of the corresponding Hopf image algebra, A = C(G) with . We study a certain family of discrete measures , coming from the idempotent state theory of G, which converge in Cesàro limit to μ. Our main result is a duality formula of type , where are the truncations of the spectral measures μ,ν associated to . We also prove, using these truncations , that for any deformed Fourier matrix we have μ = ν.
Unitaires multiplicatifs en dimension finie et leurs sous-objets
On appelle pré-sous-groupe d’un unitaire multiplicatif agissant sur un espace hilbertien de dimension finie une droite vectorielle de telle que . Nous montrons que les pré-sous-groupes sont en nombre fini, donnons un équivalent du théorème de Lagrange et généralisons à ce cadre la construction du “bi-produit croisé”. De plus, nous établissons des bijections entre pré-sous-groupes et sous-algèbres coïdéales de l’algèbre de Hopf associée à , et donc, d’après Izumi, Longo, Popa, avec les...