Residually solvable extensions of pro-nilpotent Leibniz superalgebras
L.M. CamachoDpto. Matemática Aplicada I, Universidad de Sevilla, Sevilla, SpainR.M. NavarroDpto. de Matemáticas, Universidad de Extremadura, Cáceres, SpainB. A. OmirovNational University of Uzbekistan, AKFA University, Tashkent, Uzbekistan
ABI
Аннотация
Throughout this paper we show that the method for describing finite-dimensional solvable Leibniz superalgebras with a given nilradical can be extended to infinite-dimensional ones, or so-called residually solvable Leibniz superalgebras. Prior to that, we improve the solvable extension method for the finite-dimensional case obtaining new and important results. Additionally, we fully determine the residually solvable Lie and Leibniz superalgebras with maximal codimension of pro-nilpotent ideals the model filiform Lie and null-filiform Leibniz superalgebras, respectively. Moreover, we prove that the residually solvable superalgebras obtained are complete.
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