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Using the concept of 3-Lie bialgebra, which has recently been defined inarXiv:1604.04475, we construct Bagger-Lambert-Gustavson (BLG) model forM2-brane on Manin triple of a special 3-Lie bialgebra. Then by using thecorrespondence and relation between those 3-Lie bialgebra with Lie bialgebra,we reduce this model to an $N=(4,4)$ WZW model (D2-brane), such that, itsalgebraic structure is a Lie bialgebra with one 2-cocycle. In this manner byusing correspondence of 3-Lie bialgebra and Lie bialgebra (for this special3-Lie algebra) one can construct M2-brane from a D2-brane and vice versa.

M2 to D2 and vice versa by 3-Lie and Lie bialgebra