We study actions of discrete groups on Hilbert C*-modules induced from topological actions on compact Hausdorff spaces. We show non-amenability of actions of non-amenable and non-a-T-menable groups, provided there exists a quasi-invariant probability measure which is sufficiently close to being invariant.
MSC 2010: 30C60A more general version of Hilbert's fifth problem, called the Hilbert-Smith conjecture, asserts that among all locally compact topological groups only Lie groups can act effectively on finite-dimensional manifolds. We give a solution of the Hilbert-Smith Conjecture for K - quasiconformal groups acting on domains in the extended n - dimensional Euclidean space.
In this paper, we consider several invariant complex structures on a compact real nilmanifold, and we study relations between invariant complex structures and Hodge numbers.
On a real hypersurface in of class we consider a local CR structure by choosing complex vector fields in the complex tangent space. Their real and imaginary parts span a -dimensional subspace of the real tangent space, which has dimension If the Levi matrix of is different from zero at every point, then we can generate the missing direction. Under this assumption we prove interior a priori estimates of Schauder type for solutions of a class of second order partial differential equations...
We classify compact Kähler manifolds of dimension on which acts a lattice of an almost simple real Lie group of rank . This provides a new line in the so-called Zimmer program, and characterizes certain complex tori as compact Kähler manifolds with large automorphisms groups.
Let G be the Banach-Lie group of all holomorphic automorphisms of the open unit ball in a J*-algebra of operators. Let be the family of all collectively compact subsets W contained in . We show that the subgroup F ⊂ G of all those g ∈ G that preserve the family is a closed Lie subgroup of G and characterize its Banach-Lie algebra. We make a detailed study of F when is a Cartan factor.
In this paper, we are concerned with the following problem: given a set of smooth vector fields on , we ask whether there exists a homogeneous Carnot group such that is a sub-Laplacian on . We find necessary and sufficient conditions on the given vector fields in order to give a positive answer to the question. Moreover, we explicitly construct the group law i as above, providing direct proofs. Our main tool is a suitable version of the Campbell-Hausdorff formula. Finally, we exhibit several...