  In this paper we present several multipartite quantum systems featuring the
same type of genuine (tripartite) entanglement. Based on a geometric
interpretation of the so-called $|W\rangle$ and $|GHZ\rangle$ states we show
that the classification of all multipartite systems featuring those and only
those two classes of genuine entanglement can be deduced from earlier work of
algebraic geometers. This classification corresponds in fact to classification
of fundamental subadjoint varieties and establish a connection between those
systems, well known in Quantum Information Theory and fundamental simple Lie
algebras.
