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Volume 25, Issue 5
The Decomposition and Uniqueness of $n$-Lie Superalgebras

Chunyue Wang, Qingcheng Zhang & Zhishang Zhang

Commun. Math. Res., 25 (2009), pp. 385-401.

Published online: 2021-07

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  • Abstract

In this paper, the definitions and some properties of $n$-Lie superalgebras are presented. Our main aim is to study the decomposition and uniqueness of finite dimensional $n$-Lie superalgebras with trivial center. According to the decomposition of $n$-Lie superalgebras, we obtain the decomposition of inner derivation superalgebras and derivation superalgebras respectively. Furthermore, we discuss some properties about the centroid of $n$-Lie superalgebras, so we can see its application in the decomposition of $n$-Lie superalgebras.

  • Keywords

$n$-Lie superalgebra, decomposition, indecomposition, derivation, centroid.

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COPYRIGHT: © Global Science Press

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@Article{CMR-25-385, author = {Wang , ChunyueZhang , Qingcheng and Zhang , Zhishang}, title = {The Decomposition and Uniqueness of $n$-Lie Superalgebras}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {25}, number = {5}, pages = {385--401}, abstract = {

In this paper, the definitions and some properties of $n$-Lie superalgebras are presented. Our main aim is to study the decomposition and uniqueness of finite dimensional $n$-Lie superalgebras with trivial center. According to the decomposition of $n$-Lie superalgebras, we obtain the decomposition of inner derivation superalgebras and derivation superalgebras respectively. Furthermore, we discuss some properties about the centroid of $n$-Lie superalgebras, so we can see its application in the decomposition of $n$-Lie superalgebras.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19356.html} }
TY - JOUR T1 - The Decomposition and Uniqueness of $n$-Lie Superalgebras AU - Wang , Chunyue AU - Zhang , Qingcheng AU - Zhang , Zhishang JO - Communications in Mathematical Research VL - 5 SP - 385 EP - 401 PY - 2021 DA - 2021/07 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19356.html KW - $n$-Lie superalgebra, decomposition, indecomposition, derivation, centroid. AB -

In this paper, the definitions and some properties of $n$-Lie superalgebras are presented. Our main aim is to study the decomposition and uniqueness of finite dimensional $n$-Lie superalgebras with trivial center. According to the decomposition of $n$-Lie superalgebras, we obtain the decomposition of inner derivation superalgebras and derivation superalgebras respectively. Furthermore, we discuss some properties about the centroid of $n$-Lie superalgebras, so we can see its application in the decomposition of $n$-Lie superalgebras.

Wang , ChunyueZhang , Qingcheng and Zhang , Zhishang. (2021). The Decomposition and Uniqueness of $n$-Lie Superalgebras. Communications in Mathematical Research . 25 (5). 385-401. doi:
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