On the Gel'fand-Kirillov conjecture for induced ideals in the semisimple case
Anthony Joseph (1979)
Bulletin de la Société Mathématique de France
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Anthony Joseph (1979)
Bulletin de la Société Mathématique de France
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Ch. Deninger, W. Singhof (1988)
Bulletin de la Société Mathématique de France
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L. M. Camacho, J. R. Gómez, R. M. Navarro (2000)
Extracta Mathematicae
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A. Joseph (1976)
Annales scientifiques de l'École Normale Supérieure
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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...
Peyman Niroomand (2011)
Open Mathematics
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Let L be an n-dimensional non-abelian nilpotent Lie algebra and 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.
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.