A necessary condition of co-length finiteness of Lie algebra variety in the case of zero-characteristic field

This article examines how some characteristics of Lie algebra variety like co-length are connected with the variety structure in the case of zero-characteristic field. In particular, it is proved that co-length finiteness for the variety $V$ implies the inclusion $U_2\not\subset V\subset N_sA$, where $s$ is some natural number, and, as a consequence, the polynomial growth of the variety $V$.