We consider a class of stratified groups with a CR structure and a compatible control distance. For these Lie groups we show that the space of conformal maps coincide with the space of CR and anti-CR diffeomorphisms. Furthermore, we prove that on products of such groups, all CR and anti-CR maps are product maps, up to a permutation isomorphism, and affine in each component. As examples, we consider free groups on two generators, and show that these admit very simple polynomial embeddings in CN that induce their CR structure.
|Number of pages||15|
|Journal||Proceedings of the American Mathematical Society, Series B|
|Publication status||Published - 17 Jun 2020|
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- Carnot groups
- CR mappings
- quasiconformal mappings
- conformal mappings