Strongly homotopy Lie algebras of one even and two odd dimensions

We classify strongly homotopy Lie algebras-also called L∞ algebras-of one even and two odd dimensions, which are related to 2|1-dimensional Z2-graded Lie algebras. What makes this case interesting is that there are many nonequivalent L∞ examples, in addition to the Z2-graded Lie algebra (or superalgebra) structures, yet the moduli space is simple enough that we can give a complete classification up to equivalence.