For a given configuration space $M$ and Lie algebra $g$ whose action is
defined on $M$, the space $V_{0.0}$ of weakly $g$-invariant Lagrangians (i.e.
Lagrangians whose motion equations left hand sides are $g$-invariant) is
studied.
The problem is reformulated in the 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 come to the
hierarchy in the space $V_{0.0}$:
The double filtration $V_{s.r}$ ($s=0,1,2,3,4;r=0,1$) and the homomorphisms
on every space $V_{s.r}$ are constructed.
These homomorphisms take values in cohomologies of the Lie algebra $g$ and
configuration space $M$. On one hand every space $V_{s.r}$ is the kernel of the
corresponding homomorphism, on the other hand this space is defined by its
physical properties.