Completable nilpotent Lie superalgebras

Mingzhong WU

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PDF(148 KB)
Front. Math. China ›› 2015, Vol. 10 ›› Issue (3) : 697-713. DOI: 10.1007/s11464-014-0362-x
RESEARCH ARTICLE
RESEARCH ARTICLE

Completable nilpotent Lie superalgebras

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Abstract

We discuss a class of filiform Lie superalgebras Ln,m. From these Lie superalgebras, all the other filiform Lie superalgebras can be obtained by deformations. We have decompositions of Der0¯(Ln,m) and Der1 (Ln,m). By computing a maximal torus on each Ln,m, we show that Ln,m are completable nilpotent Lie superalgebras. We also view Ln,m as Lie algebras, prove that Ln,m are of maximal rank, and show that Ln,m are completable nilpotent Lie algebras. As an application of the results, we show a Heisenberg superalgebra is a completable nilpotent Lie superalgebra.

Keywords

Filiform Lie superalgebra / Heisenberg superalgebra / completable nilpotent Lie superalgebra / maximal torus / complete Lie superalgebra

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Mingzhong WU. Completable nilpotent Lie superalgebras. Front. Math. China, 2015, 10(3): 697‒713 https://doi.org/10.1007/s11464-014-0362-x

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