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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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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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
  • MR Author ID: 54445
  • Email: dani@math.tifr.res.in
  • Received by editor(s): April 29, 2002
  • Received by editor(s) in revised form: July 12, 2002
  • Published electronically: December 4, 2002
  • © Copyright 2002 American Mathematical Society
  • 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
  • MathSciNet review: 1946401