Variational Lie algebroids and homological evolutionary vector fields

We define Lie algebroids over infinite jet spaces for vector bundles over smooth manifolds. We also establish their equivalent representation through homological evolutionary vector fields on certain infinite jet super-bundles. Our new definition is a nontrivial generalization of the classical one for usual manifolds, which is no longer applicable, and more fully grasps the geometry of strings in space-time. (The talk is based on the joint work in progress with J.van de Leur:math.DG/1006.4227v2 [4].)