Automorphisms of Non-Singular Nilpotent Lie Algebras
Journal of Lie theory, Tome 23 (2013) no. 4, pp. 1085-11
Cet article a éte moissonné depuis la source Heldermann Verlag
\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.
Classification :
17B30, 16W25
Mots-clés : Lie groups, Lie algebras, Heisenberg type groups
Mots-clés : Lie groups, Lie algebras, Heisenberg type groups
@article{JLT_2013_23_4_JLT_2013_23_4_a10,
author = {A. Kaplan and A. Tiraboschi },
title = {Automorphisms of {Non-Singular} {Nilpotent} {Lie} {Algebras}},
journal = {Journal of Lie theory},
pages = {1085--11},
year = {2013},
volume = {23},
number = {4},
url = {http://geodesic.mathdoc.fr/item/JLT_2013_23_4_JLT_2013_23_4_a10/}
}
A. Kaplan; A. Tiraboschi . Automorphisms of Non-Singular Nilpotent Lie Algebras. Journal of Lie theory, Tome 23 (2013) no. 4, pp. 1085-11. http://geodesic.mathdoc.fr/item/JLT_2013_23_4_JLT_2013_23_4_a10/