Abstract
We give a construction of homotopy algebras based on “higher derived brackets”. More precisely, the data include a Lie superalgebra with a projector on an Abelian subalgebra satisfying a certain axiom, and an odd element Δ . Given this, we introduce an infinite sequence of higher brackets on the image of the projector, and explicitly calculate their Jacobiators in terms of Δ 2 . This allows to control higher Jacobi identities in terms of the “order” of Δ 2 . Examples include Stasheff's strongly homotopy Lie algebras and variants of homotopy Batalin–Vilkovisky algebras. There is a generalization with Δ replaced by an arbitrary odd derivation. We discuss applications and links with other constructions.
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