Low-dimensional filiform lie superalgebras

Abstract

The aim of this paper is to give a classification up to isomorphism of low dimension filiform Lie superalgebras.

On Deformations of the Filiform Lie SuperalgebraLn,m

“…Proof. A cocycle f satisfies the two relations (2) and (3). A consequence of this is that f (Y m , Y m ) = a m,n X n .…”

“…At the end an evaluation of the dimension of the space Z 2 0 (L n,m , L n,m ) is established. The description of this cocycles can help us to get some classifications which was done in [2,3].…”

Classification of some nilpotent class of leibniz superalgebras

“…We define the characteristic sequence as in [5]. Let L = L 0 ⊕ L 1 be a nilpotent Leibniz superalgebra.…”

On a nilpotent lie superalgebra which generalizes Qn

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In [6] and [7] the author introduces the notion of filiform Lie superalgebras, generalizing the filiform Lie algebras studied by Vergne in the sixties. In these appers, the superalgebras whose even part is isomorphic to the model filiform Lie algebra L n are studied and classified in low dimensions.

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