On the frames of spaces of finite-dimensional Lie algebras of dimension at most 6

In this paper, the frames of spaces of complex $n$-dimensional Lie algebras (that is, the intersections of all irreducible components of these spaces) are studied. A complete description of the frames and their projectivizations for $n\le 6$ is given. It is also proved that for $n\le 6$ the projectivizations of these spaces are simply connected.
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