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Equivalence of certain free topological groups

Jan Baars (1992)

Commentationes Mathematicae Universitatis Carolinae

In this paper we give a complete isomorphical classification of free topological groups F M ( X ) of locally compact zero-dimensional separable metric spaces X . From this classification we obtain for locally compact zero-dimensional separable metric spaces X and Y that the free topological groups F M ( X ) and F M ( Y ) are isomorphic if and only if C p ( X ) and C p ( Y ) are linearly homeomorphic.

Equivariant completions

Michael Megrelishvili (1994)

Commentationes Mathematicae Universitatis Carolinae

An important consequence of a result of Katětov and Morita states that every metrizable space is contained in a complete metrizable space of the same dimension. We give an equivariant version of this fact in the case of a locally compact σ -compact acting group.

Equivariant deformation quantization for the cotangent bundle of a flag manifold

Ranee Brylinski (2002)

Annales de l’institut Fourier

Let X be a (generalized) flag manifold of a complex semisimple Lie group G . We investigate the problem of constructing a graded star product on = R ( T X ) which corresponds to a G -equivariant quantization of symbols into twisted differential operators acting on half-forms on X . We construct, when is generated by the momentum functions μ x for G , a preferred choice of where μ x φ has the form μ x φ + 1 2 { μ x , φ } t + Λ x ( φ ) t 2 . Here Λ x are operators on . In the known examples, Λ x ( x 0 ) is not a differential operator, and so the star product μ x φ ...

Ergodicité et pureté des produits de Riesz

François Parreau (1990)

Annales de l'institut Fourier

On montre que les produits de Riesz sur le tore sont des mesures ergodiques sous une condition de lacunarité pour les fréquences, indépendamment de toute propriété arithmétique, et que cette condition est la meilleure possible de ce point de vue. On établit un critère analogue pour la propriété de pureté discutés précédemment par B. Host et l’auteur, ce qui fournit l’exemple d’une mesure pure étrangère à toutes ses translatées et en particulier non ergodique.

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