Canonical subgroups of
We classify, up to conjugation, all subgroups of the semidirect products and . Our methods can also be applied to all Lie groups that are locally isomorphic to them.
Classification of CR invariant structures for compact Lie groups. (Classification des structures CR invariantes pour les groupes de Lie compacts.)
Compact fiberings of homogeneous spaces. I
Compression Semigroups of Open Orbits on Real Flag Manifolds.
Continuous transformation groups on spaces
A differentiable group is a group in the category of (reduced and nonreduced) differentiable spaces. Special cases are the rationals ℚ, Lie groups, formal groups over ℝ or ℂ; in general there is some mixture of those types, the general structure, however, is not yet completely determined. The following gives as a corollary a first essential answer. It is shown, more generally,that a locally compact topological transformation group, operating effectively on a differentiable space X (which satisfies...
Contraction semigroups and representations.
Controllability of invariant control systems at uniform time
Let be a compact and connected semisimple Lie group and an invariant control systems on . Our aim in this work is to give a new proof of Theorem 1 proved by Jurdjevic and Sussmann in [6]. Precisely, to find a positive time such that the system turns out controllable at uniform time . Our proof is different, elementary and the main argument comes directly from the definition of semisimple Lie group. The uniform time is not arbitrary. Finally, if denotes the reachable set from arbitrary...
Controllability on real reductive Lie groups.
Corners and Arithmetic Groups
Correction to the paper “Compact fiberings of homogeneous spaces. I”
Covering locally compact groups by less than many translates of a compact nullset
Gruenhage asked if it was possible to cover the real line by less than continuum many translates of a compact nullset. Under the Continuum Hypothesis the answer is obviously negative. Elekes and Stepr mans gave an affirmative answer by showing that if is the well known compact nullset considered first by Erdős and Kakutani then ℝ can be covered by cof() many translates of . As this set has no analogue in more general groups, it was asked by Elekes and Stepr mans whether such a result holds for...
Currents on Lie groups.
Curvature of a semi-direct extension of a Heisenberg type nilpotent group