  It is known that a single mapping defined on one term of a differential
graded vector space extends to a strongly homotopy Lie algebra structure on the
graded space when that mapping satisfies two conditions. This strongly homotopy
Lie algebra is nontrivial (it is not a Lie algebra); however we show that one
can obtain an sh-Lie algebra where the only nonzero mappings defining it are
the lower order mappings. This structure applies to a significant class of
examples. Moreover in this case the graded space can be replaced by another
graded space, with only three nonzero terms, on which the same sh-Lie structure
exists.
