Solvable Lie and Leibniz superalgebras with a given nilradical

Abstract Throughout this paper we show that under certain conditions the method for describing solvable Leibniz (resp. Lie) algebras with given nilradical by means of non-nilpotent outer derivations of the nilradical is also applicable to the case Leibniz (resp. Lie) superalgebras. Moreover, after having established the general method for Lie and Leibniz superalgebras, we classify all the solvable superalgebras on a very important class of each of them, that is, those with nilradical of maximal nilindex. Note that for <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>n</m:mi> <m:mo>+</m:mo> <m:mi>m</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> {(n+m)} -dimensional superalgebras this maximal nilindex is <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo>+</m:mo> <m:mi>m</m:mi> </m:mrow> <m:mo>-</m:mo> <m:mn>1</m:mn> </m:mrow> </m:math> {n+m-1} in the Lie case and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>n</m:mi> <m:mo>+</m:mo> <m:mi>m</m:mi> </m:mrow> </m:math> {n+m} in Leibniz.

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