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

References in corpus (3)

• Courant Algebroids and Strongly Homotopy Lie Algebras
• L-infinity structures on mapping cones
• Lie Atoms and their deformation theory

Cited by in corpus (12)

• $L_{\infty }$ Algebras and Field Theory
• Leibniz algebroids, twistings and exceptional generalized geometry
• The Embedding Tensor, Leibniz-Loday Algebras, and Their Higher Gauge Theories
• Tensor hierarchies and Leibniz algebras
• Nonabelian higher derived brackets
• L-infinity algebras and higher analogues of Dirac structures and Courant algebroids
• Lie and Leibniz Algebras of Lower-Degree Conservation Laws
• Nijenhuis forms on $L_{\infty }$-algebras and Poisson geometry
• Homotopy Poisson algebras, Maurer-Cartan elements and Dirac structures of CLWX 2-algebroids
• Nonlinear realisations of Lie superalgebras
• Moyal-Weyl deformations of $\mathrm{DGA}$ and $\mathrm{DGCA}$
• T-duality and exceptional generalized geometry through symmetries of dg-manifolds