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Higher derived brackets · Around

2010

Higher derived brackets

Getzler, Ezra

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We show that there is a sequence of operations on the positively graded part of a differential graded algebra making it into an L-infinity algebra.

The formulas for the higher brackets involve Bernoulli numbers.
The construction generalizes the derived bracket for Poisson manifolds, and the Lie 2-algebra associated to a Courant algebroid constructed by Roytenberg and Weinstein.

Built on

Koszul,J.-L.: Crochet de Schouten-Nijenhuis et cohomologie, In: “The mathematical heritage of Élie Cartan (Lyon, 1984),” Astérisque, Numero Hors Serie, 257–-271 (1985)
1985
Earlier work this paper cites.
Roytenberg, D., and Weinstein, A.: Courant algebroids and strongly homotopy Lie algebras, Lett. Math. Phys. 46
1998
Earlier work this paper cites.

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Fiorenza, D., and Manetti, M.: L ∞ L_{\infty} structures on mapping cones, Algebra Number Theory 1
2007
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Ran, Z.: Lie atoms and their deformations, Geom. Funct. Anal. 18
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