Residually solvable extensions of pro-nilpotent Leibniz superalgebras

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. (C) 2021 The Authors. Published by Elsevier B.V.