  This article explores \Z_2-graded L_\infinity algebra structures on a
2|1-dimensional vector space. The reader should note that our convention on the
parities is the opposite of the usual one, because we define our structures on
the symmetric coalgebra of the parity reversion of a space, so our
2|1-dimensional L_\infinity algebras correspond to the usual 1|2-dimensional
algebras.
  We give a complete classification of all structures with a nonzero degree 1
term. We also classify all degree 2 codifferentials, which is the same as a
classification of all 1|2-dimensional Z_2-graded Lie algebras. For each of
these algebra structures, we calculate the cohomology and a miniversal
deformation.
