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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Published inThe Journal of geometric analysis Vol. 28; no. 2; pp. 1477 - 1501
Main Authors Godoy Molina, Mauricio, Kruglikov, Boris, Markina, Irina, Vasil’ev, Alexander
Format Journal Article
LanguageEnglish
Published New York Springer US 01.04.2018
Springer Nature B.V
Springer
Subjects
Abstract Harmonic Analysis
Algebra
Convex and Discrete Geometry
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Geofag: 450
Geometrics: 468
Geometrikk: 468
Geometry
Geosciences: 450
Global Analysis and Analysis on Manifolds
Lie groups
Matematikk og Naturvitenskap: 400
Mathematics
Mathematics and natural science: 400
Mathematics and Statistics
Rigidity
VDP
Tanaka prolongation
condition
type algebra
17B30
Clifford module
22E60
Pseudo
17B70
Clifford algebra
Rigidity
16W55
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Summary: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.
Bibliography:Journal of Geometric Analysis
ISSN:1050-6926
1559-002X
1559-002X
DOI:10.1007/s12220-017-9875-3