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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.