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

Dani, S.

doi:10.1090/S0002-9947-02-03178-1

Some two-step and three-step nilpotent Lie groups with small automorphism groups
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by S. G. Dani PDF

Trans. Amer. Math. Soc. 355 (2003), 1491-1503 Request permission

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 also get new examples of compact manifolds covered by two-step simply connected nilpotent Lie groups which do not admit Anosov automorphisms.

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