Frechet Lie Algebroids and Their Cohomology

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We define Lie and Courant algebroids on Frechet manifolds. Moreover, we construct a Dirac structure on the generalized tangent bundle of a Frechet manifold and show that it inherits a Frechet Lie algebroid structure. We show that the Lie algebroid cohomology of the $\mathcal{B}$-cotangent bundle Lie algebroid of a weakly symplectic Frechet manifold $M$ is the Lichnerowicz-Poisson cohomology of $M$.