A Class of Strongly Homotopy Lie Algebras with Simplified sh-Lie Structures

Details A Class of Strongly Homotopy Lie Algebras with Simplified sh-Lie Structures A Class of Strongly Homotopy Lie Algebras with Simplified sh-Lie Structures

2003-08-17

arxiv.org/abs/math/0308160v1

Mathematics

Rings and Algebras

11 pages

Scientific paper

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.

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