The Bianchi variety
arXiv:1005.5355
Abstract
The totality Lie(V) of all Lie algebra structures on a vector space V over a field F is an algebraic variety over F on which the group GL(V) acts naturally. We give an explicit description of Lie(V) for dim V=3 which is based on the notion of compatibility of Lie algebra structures.
26 pages, 8 figures, to appear on Diff. Geom. Appl