Completable nilpotent Lie superalgebras

摘要

We discuss a class of filiform Lie superalgebras L~(n,m). Prom these Lie superalgebras, all the other filiform Lie superalgebras can be obtained by deformations. We have decompositions of Der_0~-(L~(n,m)) and Der_1~-(L~(n,m)). By computing a maximal torus on each L~(n,m), we show that L~(n,m) are completable nilpotent Lie superalgebras. We also view L~(n,m) as Lie algebras, prove that L~(n,m) are of maximal rank, and show that L~(n,m) are completable nilpotent Lie algebras. As an application of the results, we show a Heisenberg superalgebra is a completable nilpotent Lie superalgebra.