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

Author: S. G. Dani
Journal: Trans. Amer. Math. Soc. 355 (2003), 1491-1503
MSC (2000): Primary 22D45, 22E25; Secondary 22D40, 37D20
Published electronically: December 4, 2002
MathSciNet review: 1946401
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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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Additional Information

S. G. Dani
Affiliation: Erwin Schrödinger Institute, Boltzmanngasse 9, A-1090 Vienna, Austria
Address at time of publication: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400 005, India

Received by editor(s): April 29, 2002
Received by editor(s) in revised form: July 12, 2002
Published electronically: December 4, 2002
Article copyright: © Copyright 2002 American Mathematical Society

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