Sur le Cortex d'un groupe de Lie nilpotent

Abstract

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 $T$($\mathfrak{g}$)$\otimes$ $\mathfrak{g}$*.