Infinitesimal deformations of null-filiform Leibniz superalgebras

In this paper we describe the infinitesimal deformations of null-filiform Leibniz superalgebras over a field of zero characteristic. It is known that up to isomorphism in each dimension there exist two such superalgebras NFn,mNFn,m. One of them is a Leibniz algebra (that is m=0m=0) and the second one is a pure Leibniz superalgebra (that is m≠0m≠0) of maximum nilindex. We show that the closure of the union of orbits of single-generated Leibniz algebras forms an irreducible component of the variety of Leibniz algebras. We prove that any single-generated Leibniz algebra is a linear integrable deformation of the algebra NFnNFn. Similar results for the case of Leibniz superalgebras are obtained.