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Finite-dimensional Lie subalgebras of algebras with continuous inversion

Daniel Beltiţă, Karl-Hermann Neeb (2008)

Studia Mathematica

We investigate the finite-dimensional Lie groups whose points are separated by the continuous homomorphisms into groups of invertible elements of locally convex algebras with continuous inversion that satisfy an appropriate completeness condition. We find that these are precisely the linear Lie groups, that is, the Lie groups which can be faithfully represented as matrix groups. Our method relies on proving that certain finite-dimensional Lie subalgebras of algebras with continuous inversion commute...

Flows with Periodic Factors on Homogenous Spaces.

S.G. Dani (1987)

Monatshefte für Mathematik

Fonctions indéfiniment différentiables invariantes sur l'espace tangent d'un espace symétrique

Nouri Kamoun (1998)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Free fall motion in an invariant field of forces: the 2D-case.

Pripoae, Cristina-Liliana, Pripoae, Gabriel-Teodor (2009)

Balkan Journal of Geometry and its Applications (BJGA)

Free groups of semigroups in semi-simple Lie groups.

do Rocio, Osvaldo Germano, Santana, Alexandre J. (2004)

Portugaliae Mathematica. Nova Série

Geodesically equivalent metrics on homogenous spaces

Neda Bokan, Tijana Šukilović, Srdjan Vukmirović (2019)

Czechoslovak Mathematical Journal

Two metrics on a manifold are geodesically equivalent if the sets of their unparameterized geodesics coincide. We show that if two $G$ -invariant metrics of arbitrary signature on homogenous space $G / H$ are geodesically equivalent, they are affinely equivalent, i.e. they have the same Levi-Civita connection. We also prove that the existence of nonproportional, geodesically equivalent, $G$ -invariant metrics on homogenous space $G / H$ implies that their holonomy algebra cannot be full. We give an algorithm for...

Geometria integral de los grupos ST(n+1) y ST 1 (n+1) en el sepacio proyectivo Pn

Berenice Guerrero (1990)

Revista colombiana de matematicas

Global Parametrization of Scalar Holomorphic Coadjoint Orbits of a Quasi-Hermitian Lie Group

Benjamin Cahen (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Let $G$ be a quasi-Hermitian Lie group with Lie algebra $𝔤$ and $K$ be a compactly embedded subgroup of $G$ . Let $ξ_{0}$ be a regular element of $𝔤^{*}$ which is fixed by $K$ . We give an explicit $G$ -equivariant diffeomorphism from a complex domain onto the coadjoint orbit $𝒪 (ξ_{0})$ of $ξ_{0}$ . This generalizes a result of [B. Cahen, Berezin quantization and holomorphic representations, Rend. Sem. Mat. Univ. Padova, to appear] concerning the case where $𝒪 (ξ_{0})$ is associated with a unitary irreducible representation of $G$ which is holomorphically...