  We study the varieties of Lie algebra laws and their subvarieties of
nilpotent Lie algebra laws. We classify all degenerations of (almost all)
five-step and six-step nilpotent seven-dimensional complex Lie algebras. One of
the main tools is the use of trivial and adjoint cohomology of these algebras.
In addition, we give some new results on the varieties of complex Lie algebra
laws in low dimension.

Rings and Algebras