THÈSE DE DOCTORAT ELLOUMI Mounir Espaces duaux de ...

More documents

Recommendations

Info

30 BIBLIOGRAPHIE [Joy] I. Joy Kenneth, A description of the topology on the dual space of a nilpotent Lie group, Pac. J. Math. 112, (1984), 135-139. [Sch] I. Schochetman, The dual topology of certain group extensions. Adv. in Math. 35 (1980), no. 2, 113-128
Chapitre 2 Dual topology of the motion groups SO(n) ⋉ R n Résumé : Dans ce chapitre, on étudie la topologie de l’espace dual du produit semi-direct Mn = SO(n) ⋉ R n , n ∈ N ∗ , et en identifiant ˆ Mn à l’espace quotient des orbites coadjointes admissibles m ‡ n/Mn, on montre que cette identification est un homéomorphisme. Abstract : Let n ∈ N ∗ and let Mn = SO(n) ⋉ R n be the corresponding motion group. In this paper, we describe the topology of the dual space ˆ Mn and identifying ˆ Mn with the subspace of admissible co-adjoint orbits m ‡ n/Mn, we show that this identification is a homeomorphism. 2000 Mathematics Subject Classification : 43A40, 22D10, 22E45. Keywords : Semi-direct product, dual topology, admissible coadjoint orbit space. 2.1 Introduction. It is known that for a simply connected nilpotent Lie group and more generally for an exponential solvable Lie group G = expg, its dual space � G is homeomorphic to the space of co-adjoint orbits g ∗ /G through the Kirillov mapping (see [Lep-Lud]). If we consider semi-direct products G = K ⋉ N of compact connected Lie groups K acting on simply connected nilpotent Lie groups N, then again we have an orbit picture of the dual space of G (see [Lip]) and one can guess that the topology of � G is linked to the topology of the admissible co-adjoint orbits.
Page 1: UNIVERSITÉ PAUL VERLAINE - METZ É
Page 5 and 6: Résumé Le premier problème abord
Page 7 and 8: REMERCIEMENT Je tiens à remercier
Page 9 and 10: Table des matières 1 Généralité
Page 11 and 12: Introduction Les groupes de Lie s
Page 13 and 14: sibles. Même le cas le plus simple
Page 15 and 16: Chapitre 1 Généralités Nous donn
Page 17 and 18: 1.2 Orbites coadjointes 17 On en d
Page 19 and 20: 1.3 Représentations induites 19 D
Page 21 and 22: 1.5 Produit semi-direct compact nil
Page 23 and 24: 1.6 Théorie des orbites pour les g
Page 25 and 26: 1.7 Topologie sur le dual unitaire
Page 27 and 28: 1.7 Topologie sur le dual unitaire
Page 29: Bibliographie [Ba] L. W. Baggett, A
Page 33 and 34: 2.2 The Motion groups and their dua
Page 39 and 40: 2.4 Convergence of co-adjoint orbit
Page 47 and 48: Bibliographie [Ba] W. Baggett, A de
Page 49 and 50: Chapitre 3 On the dual topology of
Page 51 and 52: 3.2 Preliminaries. 51 3.2 Prelimina
Page 53 and 54: 3.2 Preliminaries. 53 and Ad ∗ (A
Page 55 and 56: 3.2 Preliminaries. 55 as for α > 0
Page 57 and 58: 3.3 Convergence in the quotient spa
Page 69 and 70: 3.4 Some theorems on the dual topol
Page 71 and 72: 3.5 The topology of the dual space
Page 81 and 82:
3.5 The topology of the dual space
Page 83 and 84:
3.5 The topology of the dual space
Page 85 and 86:
Bibliographie [Ba] L. W. Baggett, A
Page 87 and 88:
Chapitre 4 Flat orbits and kernels
Page 89 and 90:
4.2 Preliminaries 89 4.2 Preliminar
Page 91 and 92:
4.2 Preliminaries 91 We remark that
Page 93 and 94:
4.3 Flat Orbits 93 (π(f)η)(x) = =
Page 95 and 96:
4.3 Flat Orbits 95 As j � P ( ˜
Page 97 and 98:
4.3 Flat Orbits 97 On the other han
Page 99 and 100:
4.4 Representations Associated to F
Page 101 and 102:
Page 103 and 104:
Page 105 and 106:
Page 107 and 108:
Page 109 and 110:
Page 111:
Bibliographie [Ber-Con] M. P. Berna
show all

THÈSE DE DOCTORAT ELLOUMI Mounir Espaces duaux de ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?