Sur le cortex d'un groupe de lie nilpotent

Let g be a connected and simply connected, nilpotent Lie group. In this paper, we show that the cortex of g is a semi-algebraic set by means of a geometric characterization. It is also shown that the cortex is the image under a linear projection of a countable union of a semi-algebraic sets lying in the tensor product T(g) ⊗ g *.