Higher derived brackets

TL;DR

This paper introduces a sequence of operations on positively graded parts of differential graded algebras, forming an L-infinity algebra with brackets involving Bernoulli numbers, generalizing previous structures.

Contribution

It generalizes the derived bracket construction to a broader class of algebraic structures using Bernoulli numbers.

Findings

Constructs an L-infinity algebra from differential graded algebras.

Provides explicit formulas for higher brackets involving Bernoulli numbers.

Extends the derived bracket concept to Courant algebroids.

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.