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