Finite-dimensional nilpotent Lie superalgebras of class two and skew-supersymmetric bilinear maps

Abstract

In this article, we discuss the category ${\mathcal{S}\mathcal{N}}_2$ where the objects are finite-dimensional nilpotent Lie superalgebras of class two and the category $\mathcal{SS}\mathcal{K}\mathcal{E}$ where the objects are skew-supersymmetric bilinear maps. We establish relation between ${\mathcal{S}\mathcal{N}}_2$ and $\mathcal{SS}\mathcal{K}\mathcal{E}$. As a result, we discuss the capability of nilpotent Lie superalgebras of class two.