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Journal of Lie Theory 23 (2013), No. 4, 1085--1100
Copyright Heldermann Verlag 2013

Automorphisms of Non-Singular Nilpotent Lie Algebras

Aroldo Kaplan
Facultad de Matemática, Universidad Nacional, CIEM -- CONICET, Ciudad Universitaria, Córdoba (5000), Argentina

Alejandro Tiraboschi
Facultad de Matemática, Universidad Nacional, CIEM -- CONICET (5000), Ciudad Universitaria, Córdoba, Argentina


\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

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