Nous cherchons à comprendre pourquoi la propriété (T) de Kazhdan [Kaz67, HV89, BHV08], et plus particulièrement une forme renforcée de celle-ci introduite dans [Laf08], sont un obstacle à une démonstration de la surjectivité de l’application de Baum-Connes à coefficients arbitraires pour des groupes ayant un élément γ de Kasparov, à l’aide des méthodes connues. Nous passons d’abord en revue tro...

We introduce the concept of para-Hopf algebroid and define their cyclic cohomology in the spirit of Connes-Moscovici cyclic cohomology for Hopf algebras. Para-Hopf algebroids are closely related to, but different from, Hopf algebroids. Their definition is motivated by attempting to define a cyclic cohomology theory for Hopf algebroids in general. We show that many of Hopf algebraic structures, ...

In [3], Connes found a conformal invariant using Wodzicki’s 1-density and computed it in the case of 4-dimensional manifold without boundary. In [14], Ugalde generalized the Connes’ result to n-dimensional manifold without boundary. In this paper, we generalize the results of [3] and [14] to the case of manifolds with boundary. Subj. Class.: Noncommutative global analysis; Noncommutative differ...

In this paper we consider a family of Dirac-type operators on fibration P → B equivariant with respect to an action of an étale groupoid. Such a family defines an element in the bivariant K theory. We compute the action of the bivariant Chern character of this element on the image of Connes’ map Φ in the cyclic cohomology. A particular case of this result is Connes’ index theorem for étale grou...

In this paper we consider a family of Dirac-type operators on fibration P → B equivariant with respect to an action of an étale groupoid. Such a family defines an element in the bivariant K theory. We compute the action of the bivariant Chern character of this element on the image of Connes’ map Φ in the cyclic cohomology. A particular case of this result is Connes’ index theorem for étale grou...

We consider natural representations of the Connes-Kreimer Lie algebras on rooted trees/Feynman graphs arising from Hecke correspondences in the categories LRF ,LFG constructed by K. Kremnizer and the author. We thus obtain the insertion/elimination representations constructed by Connes-Kreimer as well as an isomorphic pair we term top-insertion/top-elimination. We also construct graded finite-d...

It has become increasingly evident, starting from the seminal paper of Bost and Connes [3] and continuing with several more recent developments ([8], [10], [12], [13], [22], [24]), that there is a rich interplay between quantum statistical mechanics and arithmetic. In the case of number fields, the symmetries and equilibrium states of the Bost–Connes system are closely linked to the explicit cl...

We define a Banach algebra A to be dual if A = (A∗) ∗ for a closed submodule A∗ of A∗. The class of dual Banach algebras includes all W ∗-algebras, but also all algebras M(G) for locally compact groups G, all algebras L(E) for reflexive Banach spaces E, as well as all biduals of Arens regular Banach algebras. The general impression is that amenable, dual Banach algebras are rather the exception...