Central extensions of some solvable Leibniz superalgebras

Abstract

This work is devoted to the study of central extensions of some solvable Leibniz superalgebras. We show that a solvable Leibniz superalgebra with non-null center can be obtained by central extension of other solvable ones of lower dimensions. Moreover, we describe the central extensions for the maximal solvable Lie superalgebras with nilradical which neither characteristically nilpotent in non-split case nor do not involve characteristically nilpotent ones as a term in split case.Additionally, we apply two different procedures to the null-filiform Leibniz superalgebra and the model filiform Lie superalgebra. On the first one, we compute its central extensions and then study the maximal solvable extension of the superalgebras obtained. However, on the second procedure, we consider first its maximal solvable superalgebra and then study its central extensions. Finally, we compare the results obtained at the end of the two procedures.