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Consider a transitive definable action of a Lie group G on a definable manifold M. Given two (locally) definable subsets A and B of M, we prove that the dimension of the intersection σ(A) ∩ B is not greater than the expected one for a generic σ ∈ G.

Absolutely Closed Lie Groups.

Morikuni Goto (1973)

Mathematische Annalen

Actions of compact connected Lie Groups with few orbit types.

Eldar Straume, Wu-yi Hsiang (1982)

Journal für die reine und angewandte Mathematik

Algèbres de Clifford symplectiques et revêtements spinoriels du groupe symplectique

A. Crumeyrolle (1974/1975)

Séminaire Jean Leray

Almost Lie groups of type ...n.

Patrick Ghanaat (1989)

Journal für die reine und angewandte Mathematik

An estimation of the controllability time for single-input systems on compact Lie Groups

Andrei Agrachev, Thomas Chambrion (2006)

ESAIM: Control, Optimisation and Calculus of Variations

Geometric control theory and Riemannian techniques are used to describe the reachable set at time t of left invariant single-input control systems on semi-simple compact Lie groups and to estimate the minimal time needed to reach any point from identity. This method provides an effective way to give an upper and a lower bound for the minimal time needed to transfer a controlled quantum system with a drift from a given initial position to a given final position. The bounds include diameters...

An infinite dimensional approach to the third fundamental theorem of Lie.

Bourgin, Richard D., Robart, Thierry P. (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

An introduction to loopoids

Janusz Grabowski (2016)

Commentationes Mathematicae Universitatis Carolinae

We discuss a concept of loopoid as a non-associative generalization of Brandt groupoid. We introduce and study also an interesting class of more general objects which we call semiloopoids. A differential version of loopoids is intended as a framework for Lagrangian discrete mechanics.

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A connected Lie group equals the square of the exponential image.

A criterion for the minimal closedness of the Lie subalgebra corresponding to a connected nonclosed Lie subgroup.

A general non-linear convexity theorem.

A mountain pass theorem for actions of compact Lie groups.

A note on central extensions of Lie groups.

A note on Lie semialgebras in $𝔰𝔩 (2, ℝ)$ .

A Poisson kernel on Heisenberg type nilpotent groups

À propos de l'article «Sur la cohomologie réelle des groupes de Lie simples réels»

A short proof of the Campbell-Hausdorff formula. (Une courte démonstration de la formule de Campbell-Hausdorff.)

A theorem on generic intersections in an o-minimal structure