Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 23 (2013), No. 4, 1085--1100Copyright Heldermann Verlag 2013 Automorphisms of Non-Singular Nilpotent Lie Algebras Aroldo Kaplan Facultad de Matemática, Universidad Nacional, CIEM -- CONICET, Ciudad Universitaria, Córdoba (5000), Argentina kaplan@famaf.unc.edu.ar Alejandro Tiraboschi Facultad de Matemática, Universidad Nacional, CIEM -- CONICET (5000), Ciudad Universitaria, Córdoba, Argentina tirabo@famaf.unc.edu.ar [Abstract-pdf] \def\n{{\frak n}} \def\Aut{\mathop{\rm Aut}\nolimits} For a real, non-singular, 2-step nilpotent Lie algebra $\n$, the group $\Aut(\n)/\Aut_0(\n)$, where $\Aut_0(\n)$ is the group of automorphisms which act trivially on the center, is the direct product of a compact group with the 1-dimensional group of dilations. Maximality of some automorphisms groups of $\n$ follows and is related to how close is $\n$ to being of Heisenberg type. For example, at least when the dimension of the center is two, $\dim \Aut(\n)$ is maximal if and only if $\n$ is of Heisenberg type. The connection with fat distributions is discussed. Keywords: Lie groups, Lie algebras, Heisenberg type groups. MSC: 17B30, 16W25 [ Fulltext-pdf  (319  KB)] for subscribers only.