CONICET | Buscador de Institutos y Recursos Humanos

For a real, non-singular, 2-step nilpotent Lie algebra N , the group Aut(N)/D , where D is the subgroup acting by dilations on the center, is compact. Its dimension is maximal if N is of Heisenberg type. When the dimension of the center is one or two, this is true if and only if it is of Heisenberg type. It is conjectured that this holds in general. Since a distribution is fat if and only if its symbol non-singular, this has consequences for the Equivalence Problem for geometries based on fat distributions.