Mauricio Godoy Molina, Boris Kruglikov, Irina Markina, Alexander Vasil'ev
Published 2016-03-01Version 1
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.
Structure constants of pseudo $H$-type algebras in some integral bases
Complete classification of $H$-type algebras: I
On some representations of nilpotent Lie algebras and superalgebras
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