Strongly Homotopy Lie Algebras of One Even and Two Odd Dimensions

Abstract

We classify strongly homotopy Lie algebras - also called L-infinity algebras - of one even and two odd dimensions, which are related to $2|1$-dimensional $Z_2$-graded Lie algebras. What makes this case interesting is that there are many nonequivalent L-infinity examples, in addition to the $Z_2$-graded Lie algebra (or superalgebra) structures, yet the moduli space is simple enough that we can give a complete classification up to equivalence.