Non-Abelian Lie algebroids over jet spaces

We associate Hamiltonian homological evolutionary vector fields  - which are the non-Abelian variational Lie algebroids' differentials - with Lie algebra-valued zero-curvature representations for partial
differential equations. At the same time, we explain why the (quantum) gauge cohomology groups arising from the BV-model for the variational Lie algebroid master-functional are equipped with a structure of usual,
non-variational Lie algebroid.
   The talk is based on the recent paper 1305.4598 (joint with A.Krutov).