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A sufficient condition for nonrigidity of Carnot groups

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Abstract

In this article we consider contact mappings on Carnot groups. Namely, we are interested in those mappings whose differential preserves the horizontal space, defined by the first stratum of the natural stratification of the Lie algebra of a Carnot group. We give a sufficient condition for a Carnot group G to admit an infinite dimensional space of contact mappings, that is, for G to be nonrigid. A generalization of Kirillov’s Lemma is also given. Moreover, we construct a new example of nonrigid Carnot group.

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Authors and Affiliations

  1. Mathematisches Institut, Universität Bern, Sidlerstr. 5, 3012, Bern, Switzerland

    Alessandro Ottazzi

  2. DIMA, Università di Genova, Via Dodecaneso 35, 16146, Genova (1), Italy

    Alessandro Ottazzi

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  1. Alessandro Ottazzi
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Correspondence to Alessandro Ottazzi.

Additional information

This research was partly supported by the Swiss National Science Foundation. The author would like to thank H. M. Reimann for the helpful advices and the constant support.

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Ottazzi, A. A sufficient condition for nonrigidity of Carnot groups. Math. Z. 259, 617–629 (2008). https://doi.org/10.1007/s00209-007-0240-2

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  • DOI: https://doi.org/10.1007/s00209-007-0240-2

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