Properties of quasi-invariant measures on topological groups and associated algebras
Property (T) and groups
We show that each group in a class of finitely generated groups introduced in [2] and [3] has Kazhdan’s property (T), and calculate the exact Kazhdan constant of with respect to its natural set of generators. These are the first infinite groups shown to have property (T) without making essential use of the theory of representations of linear groups, and the first infinite groups with property (T) for which the exact Kazhdan constant has been calculated. These groups therefore provide answers...
Property T for discrete groups in terms of their regular representation.
Property (T) for ... Factors and unitary representations of Kazhdan groups.
Proposition de structures géométriques «amplifiées» pour le traitement des systèmes de points matériels
Propriétés de mélange du flot des chambres de Weyl des groupes de Ping-Pong
Dans cet article, nous étudions le flot des chambres de Weyl d’une large classe de sous-groupe discrets d’un groupe de Lie semi-simple réel : les groupes de Ping-Pong. Nous montrons que ce flot est mélangeant relativement à la mesure de Patterson-Sullivan ; celle-ci étant infinie en rang , nous précisons cette propriété de mélange en explicitant sa vitesse dans le direction du vecteur de croissance du groupe.
Propriétés des applications quadratiques d'un espace de Hilbert dans un espace vectoriel. Applications à la théorie spectrale des opérateurs normaux et à l'image numérique d'un opérateur
Propriétés (Q) et (C). Variété commutante
Soient une variété algébrique complexe, lisse, irréductible, et deux espaces vectoriels complexes de dimension finie et un morphisme de dans l’espace Lin des applications linéaires de dans . Pour , on note et le noyau et l’image de , le morphisme de dans Lin qui associe à l’application linéaire . Soit i la dimension minimale de . On dit que ala propriété en si i est inférieur à i. Soient le dual de , S l’algèbre symétrique de , l’idéal de engendré par...
P-sets and minimal right ideals in ℕ*
Recall that a P-set is a closed set X such that the intersection of countably many neighborhoods of X is again a neighborhood of X. We show that if 𝔱 = 𝔠 then there is a minimal right ideal of (βℕ,+) that is also a P-set. We also show that the existence of such P-sets implies the existence of P-points; in particular, it is consistent with ZFC that no minimal right ideal is a P-set. As an application of these results, we prove that it is both consistent with and independent of ZFC that the shift...
Pseudo-abelian varieties
Chevalley’s theorem states that every smooth connected algebraic group over a perfect field is an extension of an abelian variety by a smooth connected affine group. That fails when the base field is not perfect. We define a pseudo-abelian variety over an arbitrary field to be a smooth connected -group in which every smooth connected affine normal -subgroup is trivial. This gives a new point of view on the classification of algebraic groups: every smooth connected group over a field is an extension...
Pseudo-coefficients très cuspideaux et K-théorie.
Pseudocompact refinements of compact group topologies.
Pseudoconcave Lie groups
Pseudodifferential analysis on continuous family groupoids.
Pseudodifferential Operators on SU(2).
Pseudokähler forms on complex Lie groups.
Pseudometrics on Ext-semigroups
This paper considers certain pseudometric structures on Ext-semigroups and gives a unified characterization of several topologies on Ext-semigroups. It is demonstrated that these Ext-semigroups are complete topological semigroups. To this end, it is proved that a metric induces a pseudometric on a quotient space with respect to an equivalence relation if it has certain invariance. We give some properties of this pseudometric space and prove that the topology induced by the pseudometric coincides...
Pseudo-Riemannian weakly symmetric manifolds of low dimension
We give a classification of pseudo-Riemannian weakly symmetric manifolds in dimensions and , based on the algebraic approach of such spaces through the notion of a pseudo-Riemannian weakly symmetric Lie algebra. We also study the general symmetry of reductive -dimensional pseudo-Riemannian weakly symmetric spaces and particularly prove that a -dimensional reductive -fold symmetric pseudo-Riemannian manifold must be globally symmetric.
Pseudotopologies with applications to one-parameter groups, von Neumann algebras, and Lie algebra representations
For any pair E,F of pseudotopological vector spaces, we endow the space L(E,F) of all continuous linear operators from E into F with a pseudotopology such that, if G is a pseudotopological space, then the mapping L(E,F) × L(F,G) ∋ (f,g) → gf ∈ L(E,G) is continuous. We use this pseudotopology to establish a result about differentiability of certain operator-valued functions related with strongly continuous one-parameter semigroups in Banach spaces, to characterize von Neumann algebras, and to establish...
Pure extensions of locally compact abelian groups