Infinitesimal deformations of null-filiform Leibniz superalgebras

Abstract

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 $N{F}^{n,m}$. One of them is a Leibniz algebra (that is $m=0$) and the second one is a pure Leibniz superalgebra (that is $m\ne 0$) of maximum nilindex. We show that the closure of 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 $N{F}^n$. Similar results for the case of Leibniz superalgebras are obtained.

11 pages

References in corpus (1)

• Formal deformations, contractions and moduli spaces of Lie algebras

Cited by in corpus (8)

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