Jet spaces over Carnot groups

• Sebastiano Nicolussi Golo ^[1] ; Benjamin Warhurst ^[2]
  1. [1] University of Jyväskylä

     University of Jyväskylä

     Jyväskylä, Finlandia

     
  2. [2] University of Warsaw

     University of Warsaw

     Warszawa, Polonia

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 39, Nº 6, 2023, págs. 2289-2330
• Idioma: inglés
• DOI: 10.4171/RMI/1439
• Enlaces
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• Resumen

  • Jet spaces over Rn have been shown to have a canonical structure of stratified Lie groups (also known as Carnot groups). We construct jet spaces over stratified Lie groups adapted to horizontal differentiation and show that these jet spaces are themselves stratified Lie groups. Furthermore, we show that these jet spaces support a prolongation theory for contact maps, and in particular, a Bäcklund type theorem holds. A byproduct of these results is an embedding theorem that shows that every stratified Lie group of step s+1 can be embedded in a jet space over a stratified Lie group of step s.