In this paper, Lie bialgebra structures on a class of not-finitely graded Lie algebras B() of Block type are investigated.By proving the triviality of the first cohomology group of B() with coefficients in its adjoint tensor module, namely, H 1 (B(), B() B()) = 0 , we obtain that all Lie bialgebra structures on B() are triangular coboundary.
Wang et al. (Thu,) studied this question.