Rigidity of 2-step Carnot groups
Abstract
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 - and -type algebras are given. In particular, we establish the relation of the so-called -condition to rigidity, and we explore these conditions in relation to pseudo -type algebras.
Cite
@article{arxiv.1603.00373,
title = {Rigidity of 2-step Carnot groups},
author = {Mauricio Godoy Molina and Boris Kruglikov and Irina Markina and Alexander Vasil'ev},
journal= {arXiv preprint arXiv:1603.00373},
year = {2017}
}
Comments
Except for minor polishing this version is enriched with two appendices concerning pseudo H-type algebras with J^2-condition. In Appendix A we relate these algebras to division algebras and their split versions. In Appendix B we relate these algebras to real graded simple Lie algebras