The isotropy lattice of a lifted action

We obtain a characterization of the isotropy lattice for the lifted action of a Lie group G on TM and $T^{1}M$ based only on the knowledge of G and its action on M. Some applications to symplectic geometry are also shown. To cite this article: M. Rodríguez-Olmos, C. R. Acad. Sci. Paris, Ser. I 343 (2006).