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Automorphismes analytiques d'un domaine de Reinhardt borné d'un espace de Banach à base

Jean-Pierre Vigué (1984)

Annales de l'institut Fourier

Dans cet article, j’étudie le groupe des automorphismes analytiques d’un domaine de Reinhardt borné d’un espace de Banach complexe à base. Je montre que, dans certains cas, ce groupe est un groupe de Lie banachique réel et je donne une classification complète des domaines de Reinhardt bornés homogènes. Pour certains espaces de Banach, je montre que les seuls automorphismes analytiques de la boule-unité ouverte sont linéaires.

Berezin-Weyl quantization for Cartan motion groups

Benjamin Cahen (2011)

Commentationes Mathematicae Universitatis Carolinae

We construct adapted Weyl correspondences for the unitary irreducible representations of the Cartan motion group of a noncompact semisimple Lie group by using the method introduced in [B. Cahen, Weyl quantization for semidirect products, Differential Geom. Appl. 25 (2007), 177--190].

Canonical subgroups of H 1 ⋊ S ⁢ L ⁢ 2 , R

Filippo De Mari, Krzysztof Nowak (2002)

Bollettino dell'Unione Matematica Italiana

We classify, up to conjugation, all subgroups of the semidirect products H 1 ⋊ S ⁢ L ⁢ 2 , R and R 2 ⋊ S ⁢ L ⁢ 2 , R . Our methods can also be applied to all Lie groups that are locally isomorphic to them.

Continuous transformation groups on spaces

K. Spallek (1991)

Annales Polonici Mathematici

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...

Controllability of invariant control systems at uniform time

Víctor Ayala, José Ayala-Hoffmann, Ivan de Azevedo Tribuzy (2009)

Kybernetika

Let G be a compact and connected semisimple Lie group and Σ an invariant control systems on G . 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 s Σ such that the system turns out controllable at uniform time s Σ . 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 A = ⋂ t > 0 A ( t , e ) denotes the reachable set from arbitrary...

Covering locally compact groups by less than 2 ω many translates of a compact nullset

Márton Elekes, Árpád Tóth (2007)

Fundamenta Mathematicae

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 C E K is the well known compact nullset considered first by Erdős and Kakutani then ℝ can be covered by cof() many translates of C E K . As this set has no analogue in more general groups, it was asked by Elekes and Stepr mans whether such a result holds for...

Existence de certaines connexions plates invariantes sur les groupes de Lie

Georges Giraud, A. Medina (1977)

Annales de l'institut Fourier

On donne une caractérisation des groupes de Lie qui admettent une connexion invariante à gauche sans courbure ni torsion et dont la forme de connexion est à valeurs dans l’algèbre adjointe. On fait le lien entre cette question et le problème de platitude de certaines G -structures invariantes à gauche sur les groupes de Lie.

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