Automorphisms of non-singular nilpotent Lie algebras

2011/11/25 by Aroldo Kaplan, Kaplan, Aroldo, Alejandro Tiraboschi +1 · 1 citation
Mathematics · #16W25 #17B30 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:16W25 #msc:17B30

paper · pdf · doi:10.48550/arxiv.1111.5965

arxiv created 2012/06/07 · arxiv updated 2012/06/08

Abstract

For a real, non-singular, 2-step nilpotent Lie algebra \mathfrakn, the group \Aut(\mathfrakn)/\Aut₀(\mathfrakn), where \Aut₀(\mathfrakn) 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 \mathfrakn follows and is related to how close is \mathfrakn to being of Heisenberg type. For example, at least when the dimension of the center is two, dim \Aut(\mathfrakn) is maximal if and only if \mathfrakn is type H. The connection with fat distributions is discussed.

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