Local Superderivations on Lie Superalgebra $\mathfrak{q}$ (n)

Abstract

Let $\mathfrak{q}$ (n) be a simple strange Lie superalgebra over the complex field ℂ. In a paper by A.Ayupov, K.Kudaybergenov (2016), the authors studied the local derivations on semi-simple Lie algebras over 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.