منابع مشابه
Information-Theoretic Inequalities on Unimodular Lie Groups
Classical inequalities used in information theory such as those of de Bruijn, Fisher, Cramér, Rao, and Kullback carry over in a natural way from Euclidean space to unimodular Lie groups. These are groups that possess an integration measure that is simultaneously invariant under left and right shifts. All commutative groups are unimodular. And even in noncommutative cases unimodular Lie groups s...
متن کاملLie group foliations: dynamical systems and integrators
Foliate systems are those which preserve some (possibly singular) foliation of phase space, such as systems with integrals, systems with continuous symmetries, and skew product systems. We study numerical integrators which also preserve the foliation. The case in which the foliation is given by the orbits of an action of a Lie group has a particularly nice structure, which we study in detail, g...
متن کاملRicci Flow on Three-dimensional, Unimodular Metric Lie Algebras
We give a global picture of the Ricci flow on the space of three-dimensional, unimodular, nonabelian metric Lie algebras considered up to isometry and scaling. The Ricci flow is viewed as a two-dimensional dynamical system for the evolution of structure constants of the metric Lie algebra with respect to an evolving orthonormal frame. This system is amenable to direct phase plane analysis, and ...
متن کاملUnitary Representations of Unimodular Lie Groups in Bergman Spaces
For an arbitrary unimodular Lie group G, we construct strongly continuous unitary representations in the Bergman space of a strongly pseudoconvex neighborhood of G in the complexification of its underlying manifold. In particular, the Bergman spaces of these manifolds are infinite-dimensional.
متن کاملLie Algebras of Vector Fields and Generalized Foliations
LIE ALGEBRAS OF VECTOR FIELDS AND GENERALIZED FOLIATIONS
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ژورنال
عنوان ژورنال: Annales de la faculté des sciences de Toulouse Mathématiques
سال: 1988
ISSN: 0240-2963
DOI: 10.5802/afst.659