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 |
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Format: | Artikel |
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. |
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ISSN: | 1050-6926 1559-002X 1559-002X |
DOI: | 10.1007/s12220-017-9875-3 |