A class of strongly homotopy Lie algebras with simplified sh-Lie structures |
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Authors: | Samer Al-Ashhab |
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Affiliation: | Department of Mathematics, University of New Orleans, New Orleans, LA 70148, United States |
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Abstract: | Given a complex that is a differential graded vector space, it is known that a single mapping defined on a space of it where the homology is non-trivial extends to a strongly homotopy Lie algebra (on the graded space) when that mapping satisfies two conditions. This strongly homotopy Lie algebra is non-trivial (it is not a Lie algebra); however we show that one can obtain an sh-Lie algebra where the only non-zero 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 non-zero terms, on which the same sh-Lie structure exists. |
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Keywords: | Primary, 16E45 secondary, 81R99, 53D99 |
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