English

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.