We prove that every homogeneous Carnot group can be lifted to a free homogeneous Carnot group. Though following the ideas of Rothschild and Stein, we give simple and self-contained arguments, providing a constructive proof, as shown in the examples.
Cite this article
Andrea Bonfiglioli, Francesco Uguzzoni, A note on lifting of Carnot groups. Rev. Mat. Iberoam. 21 (2005), no. 3, pp. 1013–1035DOI 10.4171/RMI/443