Solvable Indecomposable Extensions of Two Nilpotent Lie Algebras

Classification of 7-dimensional solvable Lie algebras having 5-dimensional nilradicals

“…By using the same method, the results for the case of dimension 6 were also achieved by Mubarakzyanov [21] and Turkowski [40]. Furthermore, results in [23,27,[29][30][31][32][33][34][35]41] show that this method seems to be very effective.…”

Residually solvable extensions of an infinite dimensional filiform Leibniz algebra

“…By using these relationships the classification of solvable extensions has been given for the following classes of nilpotent Lie algebras in low-dimensions with Abelian [29,30], Heisenberg [33], Borel [41], N-graded [9], filiform and quasifiliform nilradicals [39,40] (also see [38] and references therein). A few nilradicals cases are given in [34,35,36]. In the finite-dimensional case, the concept of filiform Lie algebra has been introduced by Vergne in [43].…”

Solvable Leibniz algebras whose nilradical is a quasi-filiform Leibniz algebra of maximum length

“…The approach to description of Lie algebras with a given nilradical is based on the method developed by Malcev in [14] and Mubarakzyanov in [15]. To descriptions of solvable Lie algebras with various types of nilradicals were devoted papers [16], [17], [19][20][21][22][23]. For the case of solvable Leibniz algebras we have similar results, that is, there are classifications of solvable Leibniz algebras with various type of nilradical, like Heisenberg nilradical [3], filiform [6], naturally graded filiform [8], [12], triangular [9], direct sum of null-filiform algebras [11], some classes of naturally graded quasi-filiform Leibniz algebras [18] etc.…”