Super-biderivations and super-commuting maps on the topological $N=2$ superconformal algebra

Abstract

Let $\mathcal{T}$ be the well-known topological $N=2$ superconformal algebra. In this paper, we prove that every super-skewsymmetric super-biderivation of $\mathcal{T}$ is inner. Based on the result of super-biderivations, we show that all the linear super-commuting maps on $\mathcal{T}$ which have the form $\psi(x)=\lambda x+f(x)c$ are not standard.