We discuss the known results on rigidity of Carnot groups using Tanaka’s prolongation theory. We also apply Tanaka’s theory to study rigidity of an extended class of H-type groups which we call J-type groups. In particular we obtain a rigidity criterion giving rise to a rigid class of J-type groups which includes the H-type groups, and thus extends the results of H.M. Reimann.We also construct a noncomplex J-type group which is nonrigid and does not satisfy the rank 1 condition over the reals.

Ottazzi, A., Warhurst, B. (2009). Algebraic prolongation and rigidity of Carnot groups. MONATSHEFTE FÜR MATHEMATIK, 162(2), 179-195 [10.1007/s00605-009-0170-7].

Algebraic prolongation and rigidity of Carnot groups

OTTAZZI, ALESSANDRO;
2009

Abstract

We discuss the known results on rigidity of Carnot groups using Tanaka’s prolongation theory. We also apply Tanaka’s theory to study rigidity of an extended class of H-type groups which we call J-type groups. In particular we obtain a rigidity criterion giving rise to a rigid class of J-type groups which includes the H-type groups, and thus extends the results of H.M. Reimann.We also construct a noncomplex J-type group which is nonrigid and does not satisfy the rank 1 condition over the reals.
Articolo in rivista - Articolo scientifico
Carnot group, H-type group, Fundamental graded algebra, Prolongation, Contact map, Differential system
English
2009
162
2
179
195
none
Ottazzi, A., Warhurst, B. (2009). Algebraic prolongation and rigidity of Carnot groups. MONATSHEFTE FÜR MATHEMATIK, 162(2), 179-195 [10.1007/s00605-009-0170-7].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/9836
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