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2006.309: Higher derived brackets and homotopy algebras

2006.309: Theodore Voronov (2005) Higher derived brackets and homotopy algebras. Journal of Pure and Applied Algebra, 202 (1-3). pp. 133-153. ISSN 0022-4049

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DOI: 10.1016/j.jpaa.2005.01.010


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 Δ2. This allows to control higher Jacobi identities in terms of the “order” of Δ2. 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.

Item Type:Article
Subjects:MSC 2000 > 16 Associative rings and algebras
MSC 2000 > 17 Nonassociative rings and algebras
MSC 2000 > 18 Category theory; homological algebra
MSC 2000 > 58 Global analysis, analysis on manifolds
MIMS number:2006.309
Deposited By:Miss Louise Stait
Deposited On:16 August 2006

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