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

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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@Article{CMR-25-385, author = {Chunyue and Wang and and 18190 and and Chunyue Wang and Qingcheng and Zhang and and 18191 and and Qingcheng Zhang and Zhishang and Zhang and and 18192 and and Zhishang Zhang}, 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.

ChunyueWang, QingchengZhang & ZhishangZhang. (2021). The Decomposition and Uniqueness of $n$-Lie Superalgebras. Communications in Mathematical Research . 25 (5). 385-401. doi:
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