My question is of course linked to physics, since I'm a student of physics.
The symmetry algebra of 3d de-sitter spacetimes is $\mathfrak{so}(3,1) \sim \mathfrak{sl}_2(\mathbb{C})$ which is also the Lorentz algebra in 4D. But Lorentz algebra can be supersymmetrized in 4D with only one grassmanian generator. What I mean by that mathematically is "the algebra can be embedded in a $\mathbb{Z}_2$ graded Lie algebra which satisfies certain axioms (see here)".
whereas literature is filled with statements (such as section II of this paper) "de Sitter algebra cannot be supersymmetrized unless we have even $\mathcal{N}$(= no. of grassmanian generators)" Why so? How does the dimension play a role in saying whether I can write a superalgebra from a lie algebra?