Invariant orders in simply connected Lie groups.
Invariant structures on the 6-dimensional generalized Heisenberg group
Invariants of complex structures on nilmanifolds
Let be a simply connected -dimensional nilpotent Lie group endowed with an invariant complex structure. We define a left invariant Riemannian metric on compatible with to be minimal, if it minimizes the norm of the invariant part of the Ricci tensor among all compatible metrics with the same scalar curvature. In [7], J. Lauret proved that minimal metrics (if any) are unique up to isometry and scaling. This uniqueness allows us to distinguish two complex structures with Riemannian data, giving...
Invertible Carnot Groups
We characterize Carnot groups admitting a 1-quasiconformal metric inversion as the Lie groups of Heisenberg type whose Lie algebras satisfy the J2-condition, thus characterizing a special case of inversion invariant bi-Lipschitz homogeneity. A more general characterization of inversion invariant bi-Lipschitz homogeneity for certain non-fractal metric spaces is also provided.
Irreducible representations of locally compact groups that cannot be Hausdorff separated from the identity representation.
Isolated Points in Duals of Certain Locally Compact Groups.
Isospectral deformations of closed riemannian manifolds with different scalar curvature
We construct the first examples of continuous families of isospectral Riemannian metrics that are not locally isometric on closed manifolds , more precisely, on , where is a torus of dimension and is a sphere of dimension . These metrics are not locally homogeneous; in particular, the scalar curvature of each metric is nonconstant. For some of the deformations, the maximum scalar curvature changes during the deformation.
Jet spaces as nonrigid Carnot groups.
Jets de fonctions differentiables sur le dual d'un groupe de Lie nilpotent.
Kontrahierende Erweiterungen und kontrahierbare Gruppen.
bounds for spectral multipliers on rank one NA-groups with roots not all positive
We consider a family of non-unimodular rank one NA-groups with roots not all positive, and we show that on these groups there exists a distinguished left invariant sub-Laplacian which admits a differentiable functional calculus for every p ≥ 1.
La formule de Plancherel pour un groupe de Lie resoluble connexe. II.
Lattices and harmonic analysis on some 2-step solvable Lie groups.
Lefschetz coincidence numbers of solvmanifolds with Mostow conditions
For any two continuous maps , between two solvmanifolds of the same dimension satisfying the Mostow condition, we give a technique of computation of the Lefschetz coincidence number of , . This result is an extension of the result of Ha, Lee and Penninckx for completely solvable case.
Leibniz's rule on two-step nilpotent Lie groups
Let be a nilpotent Lie algebra which is also regarded as a homogeneous Lie group with the Campbell-Hausdorff multiplication. This allows us to define a generalized multiplication of two functions in the Schwartz class (*), where and are the Abelian Fourier transforms on the Lie algebra and on the dual * and ∗ is the convolution on the group . In the operator analysis on nilpotent Lie groups an important notion is the one of symbolic calculus which can be viewed as a higher order generalization...
Lie algebra cohomology and generating functions.
Lie groups with no left invariant complex structures
Lp multipliers and their H1-L1 estimates on the Heisenberg group.
We give a Hörmander-type sufficient condition on an operator-valued function M that implies the Lp-boundedness result for the operator TM defined by (TMf)^ = Mf^ on the (2n + 1)-dimensional Heisenberg group Hn. Here ^ denotes the Fourier transform on Hn defined in terms of the Fock representations. We also show the H1-L1 boundedness of TM, ||TMf||L1 ≤ C||f||H1, for Hn under the same hypotheses of Lp-boundedness.
Malliavin calculus for stable processes on homogeneous groups
Let be a symmetric semigroup of stable measures on a homogeneous group, with smooth Lévy measure. Applying Malliavin calculus for jump processes we prove that the measures have smooth densities.
Marches aléatoires sur les espaces homogènes