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Sur la méthode des orbites pour une algèbre de Lie résoluble

Jean-Yves Charbonnel (1998)

Annales de l'institut Fourier

Soit 𝔤 une algèbre de Lie complètement résoluble sur un corps de caractéristique zéro. Soit Q un idéal 𝔤 -invariant de l’algèbre symétrique de 𝔤 . L’application de Dixmier pour 𝔤 associe à Q un idéal premier de l’algèbre enveloppante U ( 𝔤 ) de 𝔤 . Soit A ^ ( 𝔤 ) l’algèbre des opérateurs différentiels à coefficients séries formelles. Dans l’algèbre A ( 𝔤 ) des opérateurs différentiels à coefficients polynomiaux, il y a un idéal à gauche Λ 𝔤 ' ( Q ) qui contient Q et les champs de vecteurs adjoints. Il y a un plongement canonique...

Symplectic torus actions with coisotropic principal orbits

Johannes Jisse Duistermaat, Alvaro Pelayo (2007)

Annales de l’institut Fourier

In this paper we completely classify symplectic actions of a torus T on a compact connected symplectic manifold ( M , σ ) when some, hence every, principal orbit is a coisotropic submanifold of ( M , σ ) . That is, we construct an explicit model, defined in terms of certain invariants, of the manifold, the torus action and the symplectic form. The invariants are invariants of the topology of the manifold, of the torus action, or of the symplectic form.In order to deal with symplectic actions which are not Hamiltonian,...

The classification of two step nilpotent complex Lie algebras of dimension 8

Zaili Yan, Shaoqiang Deng (2013)

Czechoslovak Mathematical Journal

A Lie algebra 𝔤 is called two step nilpotent if 𝔤 is not abelian and [ 𝔤 , 𝔤 ] lies in the center of 𝔤 . Two step nilpotent Lie algebras are useful in the study of some geometric problems, such as commutative Riemannian manifolds, weakly symmetric Riemannian manifolds, homogeneous Einstein manifolds, etc. Moreover, the classification of two-step nilpotent Lie algebras has been an important problem in Lie theory. In this paper, we study two step nilpotent indecomposable Lie algebras of dimension 8 over the...

The existence of c-covers of Lie algebras

Mohammad Reza Rismanchian (2015)

Colloquium Mathematicae

The aim of this work is to obtain the structure of c-covers of c-capable Lie algebras. We also obtain some results on the existence of c-covers and, under some assumptions, we prove the absence of c-covers of Lie algebras.

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