The last talk we gave on this topic (in the meeting Iberian Strings 2017) was largely about the physics; here we focus on the mathematics. No prior knowledge will be assumed.

We define the process of invariant central extension: taking central extensions by cocycles invariant under a given subgroup of automorphisms of a Lie superalgebra. We give conditions that allow us to carve out the Lorentz group inside the automorphisms of Minkowski superspacetime, and prove that by successive invariant central extensions of the superpoint, we construct all superspacetimes up to dimension 11.