Rigidity of 2-Step Carnot Groups

In the present paper, we study the rigidity of 2-step Carnot groups, or equivalently, of graded 2-step nilpotent Lie algebras. We prove the alternative that depending on bi-dimensions of the algebra, the Lie algebra structure makes it either always of infinite type or generically rigid, and we speci...

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Veröffentlicht in:The Journal of Geometric Analysis 2018-04, Vol.28 (2), p.1477-1501
Hauptverfasser: Godoy Molina, Mauricio, Kruglikov, Boris, Markina, Irina, Vasil’ev, Alexander
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Sprache:eng
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Zusammenfassung:In the present paper, we study the rigidity of 2-step Carnot groups, or equivalently, of graded 2-step nilpotent Lie algebras. We prove the alternative that depending on bi-dimensions of the algebra, the Lie algebra structure makes it either always of infinite type or generically rigid, and we specify the bi-dimensions for each of the choices. Explicit criteria for rigidity of pseudo H - and J -type algebras are given. In particular, we establish the relation of the so-called J 2 -condition to rigidity, and we explore these conditions in relation to pseudo H -type algebras.
ISSN:1050-6926
1559-002X
1559-002X
DOI:10.1007/s12220-017-9875-3