We review the formulation and proof of the Baum-Connes conjecture for the dual of the quantum group of Woronowicz. As an illustration of this result we determine the K-groups of quantum automorphism groups of simple matrix algebras.
The automorphisms of a quasigroup or Latin square are permutations of the set of entries of the square, and thus belong to conjugacy classes in symmetric groups. These conjugacy classes may be recognized as being annihilated by symmetric group class functions that belong to a -ideal of the special -ring of symmetric group class functions.
Given a tuple of irreducible characters of we define a star-shaped quiver together with a dimension vector . Assume that is generic. Our first result is a formula which expresses the multiplicity of the trivial character in the tensor product as the trace of the action of some Weyl group on the intersection cohomology of some (non-affine) quiver varieties associated to . The existence of such a quiver variety is subject to some condition. Assuming that this condition is satisfied, we...
We give an explicit recollement for a cocomplete abelian category and its colimit category. We obtain some applications on Leavitt path algebras, derived equivalences and -groups.
On montre que si la conjecture de Farrell-Jones en -théorie algébrique est vérifiée alors celle de la -théorie hermitienne est équivalente à l’existence d’un entier tel que “assembly map” soit un isomorphisme en degré et .
In this note we prove some results in flat and differential -theory. The first one is a proof of the compatibility of the differential topological index and the flat topological index by a direct computation. The second one is the explicit isomorphisms between Bunke-Schick differential -theory and Freed-Lott differential -theory.
Guoliang Yu has introduced a property on discrete metric spaces and groups, which is a weak form of amenability and which has important applications to the Novikov conjecture and the coarse Baum–Connes conjecture. The aim of the present paper is to prove that property in particular examples, like spaces with subexponential growth, amalgamated free products of discrete groups having property A and HNN extensions of discrete groups having property A.
On étudie des équations fonctionnelles pour les différentielles des polylogarithmes uniformes. Un des ingrédients est l’analogue infinitésimal d’un complexe introduit par Goncharov. On obtient en particulier une équation fonctionnelle à 22 termes pour la différentielle du trilogarithme.
The classical Serre-Swan's theorem defines an equivalence between the category of vector bundles and the category of finitely generated projective modules over the algebra of continuous functions on some compact Hausdorff topological space. We extend these results to obtain a correspondence between the category of representations of an étale Lie groupoid and the category of modules over its Hopf algebroid that are of finite type and of constant rank. Both of these constructions are functorially...
One defines a Riemann-Roch natural transformation from algebraic to topological higher bivariant K-theory in the category of complex spaces.