For a compact quantum group $\mathbb {G} $ of Kac type, we study the existence of a Haar
trace-preserving embedding of the von Neumann algebra $ L^\infty (\mathbb {G}) $ into an …

We prove that the $ L^ 2$-Betti numbers of a unimodular locally compact group $ G $
coincide, up to a natural scaling constant, with the $ L^ 2$-Betti numbers of the countable …

We show that if A and H are Hopf algebras that have equivalent tensor categories of
comodules, then one can transport what we call a free Yetter–Drinfeld resolution of the …

We prove that the orthogonal free quantum group factors L (FON) are strongly 1-bounded in
the sense of Jung. In particular, they are not isomorphic to free group factors. This result is …

We prove that a compact quantum group is coamenable if and only if its corepresentation
ring is amenable. We further propose a Foelner condition for compact quantum groups and …

Cet article présente quelques résultats de la thèse de l'auteur,«L2-Betti Numbers of Locally
Compact Groups», dans laquelle la définition des nombres L2 de Betti des groupes …

Abstract We prove a Delorme–Guichardet type theorem for discrete quantum groups
expressing property (T) of the quantum group in question in terms of its first cohomology …

We compute the L 2-Betti numbers of the free C∗-tensor categories, which are the
representation categories of the universal unitary quantum groups A u (F). We show that the …

We show that the Gerstenhaber-Schack cohomology of a Hopf algebra determines its
Hochschild cohomology, and in particular its Gerstenhaber-Schack cohomological …

We study existence, uniqueness and triviality of path cocycles in the quantum Cayley graph
of universal discrete quantum groups. In the orthogonal case we find that the unique path …