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This analysis uncovers triangular coboundary structures in not-finitely graded Lie algebras, indicating their algebraic properties.
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.
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Wang et al. (2015) studied this question.
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