Higher derived brackets

Abstract

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.

Second version contains a remark of Calaque, who pointed out that our construction is a special case of the work of Fiorenza and Manetti math/0601312. Six pages