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 specify the bi-dimensions for each of the choices. Explicit criteria for rigidity of pseudo Hand J-type algebras are given. In particular, we establish the relation of the so-called J2-condition to rigidity, and we explore these conditions in relation to pseudo H-type algebras.
Accepted manuscript version. Published version available at: http://doi.org/10.1007/s12220-017-9875-3