Nijenhuis forms on Lie-infinity algebras associated to Lie algebroids

Introducing Nijenhuis forms on L∞-algebras gives a general frame to understand deformations of the latter. We give here a Nijenhuis interpretation of a deformation of an arbitrary Lie algebroid into an L∞-algebra. Then we show that Nijenhuis forms on L∞-algebras also give a short and efficient manner to understand Poisson-Nijenhuis structures and, more generally, the so-called exact Poisson quasi-Nijenhuis structures with background.