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

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

2002-04-29

arxiv.org/abs/math/0204344v1

Mathematics

Dynamical Systems

14 pages

Scientific paper

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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