Journal of Lie Theory

no. 4
Automorphisms of Non-Singular Nilpotent Lie Algebras
Journal of Lie Theory, Volume 23 (2013) no. 4, pp. 1085-1100
\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.
DOI: 10.5802/jolt.766
Classification: 17B30, 16W25
Keywords: Lie groups, Lie algebras, Heisenberg type groups 
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     author = {A. Kaplan and A. Tiraboschi},
     title = {Automorphisms of {Non-Singular} {Nilpotent} {Lie} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {1085--1100},
     year = {2013},
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     zbl = {1362.17019},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.766/}
}
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A. Kaplan; A. Tiraboschi. Automorphisms of Non-Singular Nilpotent Lie Algebras. Journal of Lie Theory, Volume 23 (2013) no. 4, pp. 1085-1100. doi: 10.5802/jolt.766

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