Completable nilpotent Lie superalgebras

doi:10.1007/s11464-014-0362-x

Front. Math. China

2015, Vol. 10

Issue (3) : 697-713 https://doi.org/10.1007/s11464-014-0362-x

RESEARCH ARTICLE

Completable nilpotent Lie superalgebras

Mingzhong WU^1,^2,^*(

)

1. Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China
2. Department of Mathematics, China West Normal University, Nanchong 637002, China

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Abstract

We discuss a class of filiform Lie superalgebras L^n,m. From these Lie superalgebras, all the other filiform Lie superalgebras can be obtained by deformations. We have decompositions of Der0ˉ(L^n,m) and Der1 (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.

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

Corresponding Author(s): Mingzhong WU

Issue Date: 01 April 2015

Cite this article:

Mingzhong WU. Completable nilpotent Lie superalgebras[J]. Front. Math. China, 2015, 10(3): 697-713.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-014-0362-x
https://academic.hep.com.cn/fmc/EN/Y2015/V10/I3/697

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