(joint work with Alexandr Mishchenko, Doklady Mathematical Sciences_68_5/1_2003 (in print))
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We prove that for any transitive unimodular invariantly oriented Lie algebroid L on acompact, oriented and connected manifold with isotropy Lie algebra g and trivial monodromy the cohomology algebra is the Poincare algebra with trivial signature. In particular, the examples of such algebroids are when M is simply connected or when OutG=IntG, for simply connected Lie group G with the Lie algebra g, or when the adjoint Lie algebra bundle g is a trivial flat bundle.