Note on the cortex of two-step nilpotent Lie algebras

الأصل · EN

In this paper, we construct an example of a family of 4d-dimensional two-step nilpotent Lie algebras (gd)d≥ ₂ so that the cortex of the dual of each gd is a projective algebraic set. More precisely, we show that the cortex of each dual gd* of gd is the zero set of a homogeneous polynomial of degree d. This example is a generalization of one given in "Irreducible representations of locally compact groups that cannot be Hausdorff separated from the identity representation" by " M.E.B. Bekka, and E. Kaniuth".