Locally conformal symplectic structures and their generalizations from the point of view of Lie algebroids

Abstract

We study locally conformal symplectic structures and their generalizations from the point of view of transitive Lie algebroids. To consider l.c.s. structures and their generalizations we use Lie algebroids with trivial adjoint Lie algebra bundle $M\times\mathbb{R}$ and $M\times\frak{g}$. We observe that important l.c.s's notions can be translated on the Lie algebroid's language. We generalize l.c.s. structures to $\frak{g}$-l.c.s. structures in which we can consider an arbitrary finite dimensional Lie algebra $\frak{g}$ instead of the commutative Lie algebra $\mathbb{R}$.