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...

This paper summarizes various interpretations of emotional arguments, with a focus on the mode argument introduced in multi-modal argumentation model (Gilbert, 1994). From there author shifts from descriptive account arguments to discussion about normative framework. Pointing out problems evaluative models mode, paradigmatic shift captured by Amenable Argumentation Approach is explained as way ...