Rendiconti del Seminario Matematico della Università di Padova


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Volume 122, 2009, pp. 99–127
DOI: 10.4171/RSMUP/122-8

Published online: 2009-12-31

Rigid Two-Step Nilpotent Lie Groups Relative to Multicontact Structures

Irene Venturi[1]

(1) Università di Genova, Italy

Let {Xi,Yk} denote a fixed basis of the Lie algebra n of a connected and simply connected nilpotent Lie group N of step two. Under a technical assumption on {Xi,Yk}, we prove that the Lie algebra M of vector fields V on N that satisfy [V,Xi] = λiXi is finite dimensional, a property that we refer to as rigidity. Our proof allows the explicit count of dim M.

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Venturi Irene: Rigid Two-Step Nilpotent Lie Groups Relative to Multicontact Structures. Rend. Sem. Mat. Univ. Padova 122 (2009), 99-127. doi: 10.4171/RSMUP/122-8