2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68332It 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.11 pagesRings and AlgebrasHigh Energy Physics - TheoryQuantum Algebra16E45; 81R99text