For a given configuration space M and Lie algebra whose action is defined on M the space V of weakly -invariant Lagrangians (i.e. Lagrangians whose motion equations left hand sides are -invariant) is studied. The problem is reformulated in terms of the double complex of Lie algebra cochains with values in the complex of Lagrangians. Calculating the cohomology of this complex using the method of spectral sequences we arrive at the hierarchy in the space V corresponding to the cohomologies of the Lie algebra and configuration space M. This hierarchy reflects properties of corresponding quantum mechanical Hamiltonians.