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.
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Communicated by K. Schmidt.
Ben Warhurst was supported by ARC Discovery grant “Geometry on Nilpotent Groups” and the Institute of Mathematics of the Polish Academy of Sciences.
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Ottazzi, A., Warhurst, B. Algebraic prolongation and rigidity of Carnot groups. Monatsh Math 162, 179–195 (2011). https://doi.org/10.1007/s00605-009-0170-7
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DOI: https://doi.org/10.1007/s00605-009-0170-7