Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9497185 | Journal of Pure and Applied Algebra | 2005 | 21 Pages |
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 Î. Given this, we introduce an infinite sequence of higher brackets on the image of the projector, and explicitly calculate their Jacobiators in terms of Î2. This allows to control higher Jacobi identities in terms of the “order” of Î2. Examples include Stasheff's strongly homotopy Lie algebras and variants of homotopy Batalin-Vilkovisky algebras. There is a generalization with Î replaced by an arbitrary odd derivation. We discuss applications and links with other constructions.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Theodore Voronov,