The Evens-Lu-Weinstein representation (Q A, D) for a Lie algebroid A on a manifold M is studied in the transitive case. To consider at the same time non-oriented manifolds as well, this representation is slightly modified to (Q Aor, Dor) by tensoring by orientation flat line bundle, Q Aor=QA⊗or (M) and D or=D⊗∂Aor. It is shown that the induced cohomology pairing is nondegenerate and that the representation (Q Aor, Dor) is the unique (up to isomorphy) line representation for which the top group of...

Each Lie algebra $ℱ$ of vector fields (e.g. those which are tangent to a foliation) of a smooth manifold $M$ définies, in a natural way, a spectral sequence $E_k\left(ℱ\right)$ which converges to the de Rham cohomology of $M$ in a finite number of steps. We prove e.g. that for all $k\ge 0$ there exists a foliated compact manifold with $E_k\left(ℱ\right)$ infinite dimensional.