Géométrie Des Groupes Oscillateurs Et Variétés Lo- Calement Symétriques
نویسنده
چکیده
The Oscillator Groups,Gλ, are the only solvable, non commutative, simply connected Lie groups to admit a Lorentzian bi-invariant metric. For these groups, we give sufficient conditions for a left-invariant pseudo-Riemannian metric to be complete, we determine the group of isometries, we exhibit a left-invariant affine structure and prove that it is not Lorentzian. As an application, we provide new examples of compact pseudoRiemannian (sometimes Lorentzian) locally symmetric, occasionally affine, manifolds, complete or incomplete.
منابع مشابه
Deodhar Elements in Kazhdan-Lusztig Theory
The Kazhdan-Lusztig polynomials for finite Weyl groups arise in representation theory as well as the geometry of Schubert varieties. It was proved very soon after their introduction that they have nonnegative integer coefficients, but no simple all positive interpretation for them is known in general. Deodhar has given a framework, which generally involves recursion, to express the Kazhdan-Lusz...
متن کاملGeometric aspects of rings and representations theories
Lors de la quantification algébrique d'une algèbre de Pois-son, il est intéressant que certains groupes de (co)homologie suivent cette déformation de Poisson en Hochschild. Nous présenterons ce thème relative-ment au groupe des traces en donnant des exemples provenant de variétés quotients par l'action de groupes finis, typiquement pour les singularités de Klein, les actions doublées de groupes...
متن کاملSur certains modules gradués associés aux produits symétriques
Résumé On étudie certains anneaux et modules gradués qui apparaissent en géométrie algébrique (produits symétriques) et en théorie des représentations (pléthysme). Comme applications, on obtient une description des puissances de Schur des SL(2, )-modules simples ; une action de GL(2, ) dans la représentation régulière du groupe symétrique, qui raffine la graduation bien connue de cette représen...
متن کاملTwistor and Killing Spinors in Lorentzian Geometry
— This paper is a survey of recent results concerning twistor and Killing spinors on Lorentzian manifolds based on lectures given at CIRM, Luminy, in June 1999, and at ESI, Wien, in October 1999. After some basic facts about twistor spinors we explain a relation between Lorentzian twistor spinors with lightlike Dirac current and the Fefferman spaces of strictly pseudoconvex spin manifolds which...
متن کاملGroup Schemes out of Birational Group Laws , Néron Models
— In this note, we present the theorem of extension of birational group laws in both settings of classical varieties (Weil) and schemes (Artin). We improve slightly the original proof and result with a more direct construction of the group extension, a discussion of its separation properties, and the systematic use of algebraic spaces. We also explain the important application to the constructi...
متن کامل