  This article explores L_Infinity structures -- also known as 'strongly
homotopy Lie algebras' -- on 3-dimensional vector spaces with both Z- and
Z_2-gradings. Since the Z-graded L_Infinity algebras are special cases of
Z_2-graded algebras in the induced Z_2-grading, there are generally fewer
Z-graded L_Infinity structures on a given space. On the other hand, only degree
zero automorphisms, rather than just even automorphisms, are used to determine
equivalence in a Z-graded space. We therefore find nontrivial examples in which
the map from the Z-graded moduli space to the Z_2-graded moduli space is
bijective, injective but not surjective, or surjective but not injective.
Additionally, we study how the codifferentials in the moduli spaces deform into
other nonequivalent codifferentials, which gives each moduli space a sort of
topology.
