Automorphisms of non-singular nilpotent Lie algebras

KAPLAN , AROLDO; TIRABOSCHI, ALEJANDRO

JOURNAL OF LIE THEORY

HELDERMANN VERLAG

Lugar: Lemgo; Año: 2013 vol. 23 p. 1085 - 1100

0949-5932

For a real, non-singular, 2-step nilpotent Lie algebra $mathfrak{n}$, the group Aut(mathfrak{n})/Aut_0(mathfrak{n})$, where $Aut_0(mathfrak{n})$ 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 $mathfrak{n}$ follows and is related to how close is $mathfrak{n}$ to being of Heisenberg type. For example, at least when the dimension of the center is two, $dim Aut(mathfrak{n})$ is maximal if and only if $mathfrak{n}$ is type $H$. The connection with fat distributions is discussed