On characterizing nilpotent Lie algebras by their multiplier, $$s(L)=4$$

Abstract

Let L be an n-dimensional non-abelian nilpotent Lie algebra andwhere M(L) is the Schur multiplier of a Lie algebra L. The structures of nilpotent Lie algebras L when s(L) ∈ {0, 1, 2, 3, 4, 5} are determined. In this paper, we classify all non-abelian nilpotent Lie algebras L when s(L) = 6, 7.

Characterizing Nilpotent Associative Algebras by Their Multiplier

“…There has been great success in characterizing nilpotent Lie and Leibniz algebras by invariants related to the dimension of their multipliers (see [1,2,4,5,7,8,14]). Generally, these arguments consider a measure of how far the dimension of the multiplier M (L) is from being maximal and proceed to classify algebras based on this distance.…”

CHARACTERIZATION OF FINITE DIMENSIONAL NILPOTENT LIE ALGEBRAS BY THE DIMENSION OF THEIR SCHUR MULTIPLIERS, s(L) = 5

“…It not only improves the bound of Moneyhun but also let us ask the same natural question about the characterization of Lie algebras in term of size s(L). The answer to this question was given by several papers in [15,22,23] for s(L) ≤ 4 and for s(L) ≤ 15 when conditions are put on L in [24].…”

“…It is not easy to characterize the nilpotent Lie algebras for s(L) ≥ 4 by using the only methods of previous articles [13,22,23]. Thanks to a result of [18] and the classification of indecomposable Lie algebras of Gong [10], here we are able to characterize the structure of all nilpotent Lie algebras L for s(L) = 5.…”

“…We state some results without proof and refer the reader to see [14,15,20,23]. We recall that the Lie algebras 27B and 27A in [10] are expressed by different notations L 1 and L 2 in the following proposition, respectively.…”

Characterization of finite dimensional nilpotent Lie algebras by the dimension of their Schur multipliers, $s(L)=5$

“…It not only improves the bound of Moneyhun but also let us ask the same natural question about the characterization of Lie algebras in term of size s(L). The answer to this question was given by several papers in [11,17,18] for s(L) ≤ 4 and for s(L) ≤ 15 when conditions are put on L in [19].…”