Theodore Voronov (UMIST)
theodore.voronov@umist.ac.uk The construction of a "derived bracket" is implicit in many important formulas of differential geometry and algebra. It was explicitly introduced and studied in 1990s by Y. Kosmann-Schwarzbach (using some ideas of Koszul) and by the speaker.
In this talk I will describe a new construction of "higher derived brackets" and show that it generates so-called L∞ algebras (= Stasheff's strong homotopy Lie algebras) and similar algebras from simple data. Examples include higher odd Poisson brackets generated by a differential operator of order >2, making a particular case of a "homotopy Batalin--Vilkovisky algebra".