Frechet Lie Algebroids and Their Cohomology

Abstract

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 $M$.