More on cancellative semigroups on manifolds.
In 2005, the paper [KPT05] by Kechris, Pestov and Todorcevic provided a powerful tool to compute an invariant of topological groups known as the universal minimal flow. This immediately led to an explicit representation of this invariant in many concrete cases. However, in some particular situations, the framework of [KPT05] does not allow one to perform the computation directly, but only after a slight modification of the original argument. The purpose of the present paper is to supplement [KPT05]...
We show that there exists an Abelian topological group such that the operations in cannot be extended to the Dieudonné completion of the space in such a way that becomes a topological subgroup of the topological group . This provides a complete answer to a question of V.G. Pestov and M.G. Tkačenko, dating back to 1985. We also identify new large classes of topological groups for which such an extension is possible. The technique developed also allows to find many new solutions to the...
Let G be a second countable locally compact nilpotent group. It is shown that for every norm completely mixing (n.c.m.) random walk μ, αμ + (1-α)ν is n.c.m. for 0 < α ≤ 1, ν ∈ P(G). In particular, a generic stochastic convolution operator on G is n.c.m.
On montre, pour une classe particulière de groupes non-unimodulaires , où est un groupe de Lie stratifié et où l’action de est définie par les dilatations naturelles de , et pour les sous-laplaciens invariants à gauche correspondants , que toute fonction possédant un support compact dans définit un opérateur borné sur les espaces de Lebesgue associés à la mesure de Haar invariante à droite sur , .
We define a category containing the discrete quantum groups (and hence the discrete groups and the duals of compact groups) and the compact quantum groups (and hence the compact groups and the duals of discrete groups). The dual of an object can be defined within the same category and we have a biduality theorem. This theory extends the duality between compact quantum groups and discrete quantum groups (and hence the one between compact abelian groups and discrete abelian groups). The objects in...