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Hohm, Olaf; Kupriyanov, Vladislav; Lüst, Dieter; Traube, Andmatthias (2018): Constructions of L-infinity Algebras and Their Field Theory Realizations. In: Advances in Mathematical Physics, Vol. 2018, 9282905
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Abstract

We construct L-infinity algebras for general "initial data" given by a vector space equipped with an antisymmetric bracket not necessarily satisfying the Jacobi identity. We prove that any such bracket can be extended to a 2-term L-infinity algebra on a graded vector space of twice the dimension, with the 3-bracket being related to the Jacobiator. While these L-infinity algebras always exist, they generally do not realize a nontrivial symmetry in a field theory. In order to define L-infinity algebras with genuine field theory realizations, we prove the significantly more general theorem that if the Jacobiator takes values in the image of any linear map that defines an ideal there is a 3-term L-infinity algebra with a generally nontrivial 4-bracket. We discuss special cases such as the commutator algebra of octonions, its contraction to the "R-flux algebra," and the Courant algebroid.