  Constructing M2-brane and its boundary conditions from D2-brane and the
related boundary conditions and vice versa has been possible in our recent work
by using 3-Lie bialgebra for BLG model with N = 8 supersymmetry. This could be
generalized for BL model with N = 6 by the concept of the 3-Leibniz bialgebra.
The 3-Lie bialgebra is an especial case of 3-Leibniz bialgebra, then more
comprehensive information will be obtained in this work. Consequently,
according to the correspondence of these 3-Leibniz bialgebras with Lie
bialgebras, we reduce to D2-brane such that with some restrictions on the gauge
field this D2-brane is related to the bosonic sector of an N = (4,4) WZW model
equipped with one 2-cocycle in its Lie bialgebra structure. Moreover, the
Basu-Harvey equation which is found by considering boundary conditions for BL
model containing Leibniz bialgebra structure is reduced to Nahm equation and
vice versa using this correspondence.
