Czechoslovak Mathematical Journal, first online, pp. 1-15

Local superderivations on Lie superalgebra $\mathfrak{q}(n)$

Haixian Chen, Ying Wang

Received November 20, 2016.   First published March 2, 2018.

Abstract:  Let $\mathfrak{q}(n)$ be a simple strange Lie superalgebra over the complex field $\mathbb{C}$. In a paper by A. Ayupov, K. Kudaybergenov (2016), the authors studied the local derivations on semi-simple Lie algebras over $\mathbb{C}$ and showed the difference between the properties of local derivations on semi-simple and nilpotent Lie algebras. We know that Lie superalgebras are a generalization of Lie algebras and the properties of some Lie superalgebras are similar to those of semi-simple Lie algebras, but $\mathfrak{p}(n)$ is an exception. In this paper, we introduce the definition of the local superderivation on $\mathfrak{q}(n)$, give the structures and properties of the local superderivations of $\mathfrak{q}(n)$, and prove that every local superderivation on $\mathfrak{q}(n)$, $n>3$, is a superderivation.
Keywords:  simple Lie superalgebra; superderivation; local superderivation
Classification MSC:  16W55, 17B20, 17B40
DOI:  10.21136/CMJ.2018.0597-16

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Affiliations:   Ying Wang (corresponding author), Haixian Chen, School of Mathematical Sciences, Dalian University of Technology, No.2 Linggong Road, Ganjingzi District, Dalian City, Liaoning Province, P.R.China, 116024, e-mail:,

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