Some two-step and three-step nilpotent Lie groups with small automorphism groups

2002/04/29 by S. G. Dani, Dani, S. G.
Mathematics · #22D45 #22E25 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #Finite Group Theory Research #math.DS #msc:22D45 #msc:22E25

paper · pdf · doi:10.48550/arxiv.math/0204344

14 pages

arxiv created 2002/04/29 · openalex publication_date 2002/04/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct examples of two-step and three-step nilpotent Lie groups whose automorphism groups are `small' in the sense of either not having a dense orbit for the action on the Lie group, or being nilpotent (the latter being stronger). From the results we get also new examples of compact manifolds covered by two-step simply connected Lie groups, which do not admit Anosov automorphisms.

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