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Voronov, Theodore

Higher derived brackets and homotopy algebras. (English) Zbl 1086.17012

J. Pure Appl. Algebra 202, No. 1-3, 133-153 (2005).
Here is a rather general algebraic construction producing strong homotopy Lie algebras from simple data: a Lie algebra with a projector on an abelian subalgebra satisfying a condition on commutators and an odd element \(\Delta\).
Then we have an infinity sequence of higher brackets on the image of the projector and an explicit calculation of their jacobiators in terms of \(\Delta^2\).
The main result has nice examples and applications: generalization of classical Poisson-Schouten structures, Stasheff strongly homotopy Lie algebras, variants of homotopy Batalin-Vilkovsky algebras (which appears in the physical string theory).
Links with other structures and perspectives for further studies are also discussed.
Reviewer: Georges Hoff (Villetaneuse)

Cited in 6 Reviews
Cited in 141 Documents

MSC:

17B55 Homological methods in Lie (super)algebras
18G55 Nonabelian homotopical algebra (MSC2010)
58C50 Analysis on supermanifolds or graded manifolds

Keywords:

homotopy algebras; higher brackets; jacobiators
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References:

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