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Displaying similar documents to “Symplectic structure in the enveloping algebra of a Lie algebra”

An extension of Rais' theorem and seaweed subalgebras of simple Lie algebras

Dmitri I. Panyushev (2005)

Annales de l’institut Fourier

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We prove an extension of Rais' theorem on the coadjoint representation of certain graded Lie algebras. As an application, we prove that, for the coadjoint representation of any seaweed subalgebra in a general linear or symplectic Lie algebra, there is a generic stabiliser and the field of invariants is rational. It is also shown that if the highest root of a simple Lie algerba is not fundamental, then there is a parabolic subalgebra whose coadjoint representation...

On dimension of the Schur multiplier of nilpotent Lie algebras

Peyman Niroomand (2011)

Open Mathematics

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Let L be an n-dimensional non-abelian nilpotent Lie algebra and s ( L ) = 1 2 ( n - 1 ) ( n - 2 ) + 1 - dim M ( L ) where M(L) is the Schur multiplier of L. In [Niroomand P., Russo F., A note on the Schur multiplier of a nilpotent Lie algebra, Comm. Algebra (in press)] it has been shown that s(L) ≥ 0 and the structure of all nilpotent Lie algebras has been determined when s(L) = 0. In the present paper, we will characterize all finite dimensional nilpotent Lie algebras with s(L) = 1; 2.

Some properties of complex filiform Lie algebras.

F. J. Echarte Reula, J. R. Gómez Martín, J. Núñez Valdés (1992)

Extracta Mathematicae

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The purpose of this paper is to study some properties of Filiform Lie Algebras (FLA) and to prove the following theorem: a FLA, of dimension n, is either derived from a Solvable Lie Algebra (SLA) of dimension n+1 or not derived from any LA.