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

Abstract
We construct Linfinity 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 2term Linfinity algebra on a graded vector space of twice the dimension, with the 3bracket being related to the Jacobiator. While these Linfinity algebras always exist, they generally do not realize a nontrivial symmetry in a field theory. In order to define Linfinity 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 3term Linfinity algebra with a generally nontrivial 4bracket. We discuss special cases such as the commutator algebra of octonions, its contraction to the "Rflux algebra," and the Courant algebroid.