  We introduce coG_2-vector fields, coRochesterian 2-forms and coRochesterian
vector fields on manifolds with a coclosed G_2-structure as a continuous of
work from [15], and we show that the spaces of coG_2-vector fields and of
coRochesterian vector fields are Lie subalgebras of the Lie algebra of vector
fields with the standard Lie bracket. We also define a bracket operation on the
space of coRochesterian 2-forms associated to the space of coRochesterian
vector fields and prove, despite the lack of a Jacobi identity, a relationship
between this bracket and so-called coG_2-morphisms.
