New preprint ``On the homotopy invariance of the twisted Lie algebroid cohomology'', joint with Rosa Marchesini.

The preprint ``On the homotopy invariance of the twisted Lie algebroid cohomology'', which is joint with Rosa Marchesini, has appeared on arxiv.org.

Twisted Lie algebroid cohomologies, i.e. with values in representations, are shown to be Lie algebroid homotopy-invariant. Several important classes of examples are discussed. As an application, a generalized version of the Poincaré lemma is given in the transitive case. Together with the Mayer-Vietoris theorem, which holds in this more general context as well, this leads to a Künneth formula for the cohomologies of Lie algebroids with values in representations.