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

DOI:
https://doi.org/10.1090/S0002-9947-02-03178-1

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

Email:
dani@math.tifr.res.in

DOI:
https://doi.org/10.1090/S0002-9947-02-03178-1

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