Rigidity of Iwasawa nilpotent Lie groups via Tanaka’s theory


We provide a new proof to the known result on rigidity of Iwasawa nilpotent Lie groups [5, 12]. More precisely, we use Tanaka’s prolongation theory for establishing the rigidity type of those nilpotent groups. This note aims to complement [8], where we use the point of view of Tanaka prolongations for studying rigidity in the general setting of nilpotent stratified Lie groups. When the group is of Iwasawa type, a special formalism occurs, which is related to the theory of semisimple Lie groups, namely the formalism of root systems. We use this language in order to classify the rigidity types.

DOI Code: 10.1285/i15900932v30n1p141

Simple Lie groups and algebras; contact map; prolongation; H-type algebras; differential system

Classification: 22E25; 22E60; 53C17; 58A17; 58D05

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