“…Note that the universal enveloping algebra A e of a Poisson bialgebra A is a bialgebra, as an extension, we prove the following result: It should be noted that the universal enveloping algebra A e of a DG Poisson Hopf algebra A is just a DG bialgebra. But in some special cases, A e can be endowed with the Hopf structure, such that A e becomes a DG Hopf algebra: (1) ), a (2) } = 0, where ∆(a) = a (1) ⊗ a (2) for all a ∈ A, if and only if (A e , u e , η e , ∆ e , ε e , S e , d e ) is a DG Hopf algebra.…”