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The Leibniz algebras whose subalgebras are ideals

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Kurdachenko L. A., Semko N. N., Subbotin I. Y.

Open Mathematics

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2017

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tom 15

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nr 1

92-100

EN

In this paper we obtain the description of the Leibniz algebras whose subalgebras are ideals.

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Solvable Leibniz algebras with NF n ⊕ [...] F m 1 $\begin{array}{} F_{m}^{1} \end{array} $ nilradical

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Camacho L. M., Omirov B. A., Masutova K. K., Rikhsiboev I. M.

Open Mathematics

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2017

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tom 15

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nr 1

1371-1388

EN

All finite-dimensional solvable Leibniz algebras L, having N = NFn⊕ [...] Fm1 $\begin{array}{} F_{m}^{1} \end{array} $ as the nilradical and the dimension of L equal to n+m+3 (the maximal dimension) are described. NFn and [...] Fm1 $\begin{array}{} F_{m}^{1} \end{array} $ are the null-filiform and naturally graded filiform Leibniz algebras of dimensions n and m, respectively. Moreover, we show that these algebras are rigid.

3

On dimension of the Schur multiplier of nilpotent Lie algebras

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Niroomand P.

Open Mathematics

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2011

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tom 9

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nr 1

57-64

EN

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.

Ograniczanie wyników

3 Open Mathematics

1 Camacho L. M.

1 Kurdachenko L. A.

1 Masutova K. K.

1 Niroomand P.

1 Omirov B. A.

1 Rikhsiboev I. M.

1 Semko N. N.

1 Subbotin I. Y.

2 2017

1 2011

The Leibniz algebras whose subalgebras are ideals

Solvable Leibniz algebras with NF n ⊕ [...] F m 1 $\begin{array}{} F_{m}^{1} \end{array} $ nilradical

On dimension of the Schur multiplier of nilpotent Lie algebras