Models of finite group actions.
Morita equivalence of groupoid C*-algebras arising from dynamical systems
We show that the stable C*-algebra and the related Ruelle algebra defined by I. Putnam from the irreducible Smale space associated with a topologically mixing expanding map of a compact metric space are strongly Morita equivalent to the groupoid C*-algebras defined directly from the expanding map by C. Anantharaman-Delaroche and V. Deaconu. As an application, we calculate the K⁎-group of the Ruelle algebra for a solenoid.
Morita equivalence of measured quantum groupoids. Application to deformation of measured quantum groupoids by 2-cocycles
In a recent article, Kenny De Commer investigated Morita equivalence between locally compact quantum groups, in which a measured quantum groupoid, of basis ℂ², was constructed as a linking object. Here, we generalize all these constructions and concepts to the level of measured quantum groupoids. As for locally compact quantum groups, we apply this construction to the deformation of a measured quantum groupoid by a 2-cocycle.
Multipliers of Imprimitivity Bimodules and Morita Equivalence of Crossed Products.
Nombres de Betti et facteurs de type
Damien Gaboriau a montré récemment que les nombres de Betti des feuilletages mesurés à feuilles contractiles sont des invariants de la relation d’équivalence associée. Sorin Popa a utilisé ce résultat joint à des propriétés de rigidité des facteurs de type II pour en déduire l’existence de facteurs de type II dont le groupe fondamental est trivial.
Noncommutative Cartan subalgebras of C*-algebras.
Non-commutative entropy computations for continuous fields and cross-products
We present here two non-commutative situations where dynamical entropy estimates are possible. The first result is concerned with automorphisms of cross-products by an exact group that commute with the group action and generalizes the result known for amenable groups. The second is about continuous fields of C-algebras and -automorphisms. Each result relies on explicit factorization via matrices.
Non-equilibrium phase transitions, coherence and chaos
We present a scheme for the theory of phase transitions in open dissipative systems, and show that its demands are fulfilled by quantum stochastic models of open systems, such as the laser.
Of-groups of crossed products by groups acting on trees.
On a Dimension for a Class of Homeomorphism Groups.
On automorphisms of type Arveson systems (probabilistic approach).
On -algebras associated to certain endomorphisms of discrete groups.
On certain properties of the relative entropy of states of operator algebras.
On derivations and crossed homomorphisms
We discuss some results about derivations and crossed homomorphisms arising in the context of locally compact groups and their group algebras, in particular, L¹(G), the von Neumann algebra VN(G) and actions of G on related algebras. We answer a question of Dales, Ghahramani, Grønbæk, showing that L¹(G) is always permanently weakly amenable. Then we show that for some classes of groups (e.g. IN-groups) the homology of L¹(G) with coefficients in VN(G) is trivial. But this is no longer true, in general,...
On measure theoretical analogues of the Takesaki structure theorem for type III factors
The orbit equivalence of type ergodic equivalence relations is considered. We show that it is equivalent to the outer conjugacy problem for the natural trace-scaling action of a countable dense ℝ-subgroup by automorphisms of the Radon-Nikodym skew product extensions of these relations. A similar result holds for the weak equivalence of arbitrary type cocycles with values in Abelian groups.
On Neveu decomposition and ergodic type theorems for semi-finite von Neumann algebras.
On relative amenability for von Neumann algebras
On subrelations of ergodic measured type III equivalence relations
We discuss the classification up to orbit equivalence of inclusions 𝑆 ⊂ ℛ of measured ergodic discrete hyperfinite equivalence relations. In the case of type III relations, the orbit equivalence classes of such inclusions of finite index are completely classified in terms of triplets consisting of a transitive permutation group G on a finite set (whose cardinality is the index of 𝑆 ⊂ ℛ), an ergodic nonsingular ℝ-flow V and a homomorphism of G to the centralizer of V.
On the dual weights for crossed products of von Neumann algebras II.
On the dual weights for crossed products of von Neumann algebras I.