Revista Matemática Iberoamericana

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Volume 21, Issue 3, 2005, pp. 1013–1035
DOI: 10.4171/RMI/443

Published online: 2005-12-31

A note on lifting of Carnot groups

Andrea Bonfiglioli[1] and Francesco Uguzzoni[2]

(1) Università di Bologna, Italy
(2) Università di Bologna, Italy

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.

Keywords: Lifting of vector fields, Carnot groups, fundamental solutions, free groups

Bonfiglioli Andrea, Uguzzoni Francesco: A note on lifting of Carnot groups. Rev. Mat. Iberoam. 21 (2005), 1013-1035. doi: 10.4171/RMI/443