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On dimension of the Schur multiplier of nilpotent Lie algebras
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Abstract
Let L be an n-dimensional non-abelian nilpotent Lie algebra and $$
s(L) = \frac{1}
{2}(n - 1)(n - 2) + 1 - \dim M(L)
$$ 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.
Title: On dimension of the Schur multiplier of nilpotent Lie algebras
Description:
Abstract
Let L be an n-dimensional non-abelian nilpotent Lie algebra and $$
s(L) = \frac{1}
{2}(n - 1)(n - 2) + 1 - \dim M(L)
$$ 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.
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