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

summary: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