Corrigendum: cubic polynomials on Lie groups: reduction of the Hamiltonian system

Abstract

The purpose of this corrigendum is to replace lemma 6 on page 13 of the paper to guarantee the accuracy of other results derived from it, in particular, the discussion after remark 4 on page 15. In the original version, the result we prove does not allow us to conclude, as we claim, that the set of constants of the motion we identify can be used with the Lie–Cartan theorem. The formulation of the lemma is misleading. Besides, we need the additional hypothesis that G is semisimple to be able to prove the correct statement. Therefore, both the statement and the proof should be replaced by the following.