  Emphasizing the role of Gerstenhaber algebras and of higher derived brackets
in the theory of Lie algebroids, we show that the several Lie algebroid
brackets which have been introduced in the recent literature can all be defined
in terms of Poisson and pre-symplectic functions in the sense of Roytenberg and
Terashima. We prove that in this very general framework there exists a
one-to-one correspondence between non-degenerate Poisson functions and
symplectic functions. We determine the differential associated to a Lie
algebroid structure obtained by twisting a structure with background by both a
Lie bialgebra action and a Poisson bivector.
