Automorphisms of non-singular nilpotent Lie algebras

Details Automorphisms of non-singular nilpotent Lie algebras Automorphisms of non-singular nilpotent Lie algebras

2011-11-25

arxiv.org/abs/1111.5965v1

Mathematics

Differential Geometry

Scientific paper

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.

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