Algebraic structures of N = (4, 4) and N = (8, 8) supersymmetric (SUSY) two dimensional sigma models on Lie groups (in general) and SUSY Wess-Zumino-Witten (WZW) models (as special) are obtained. For SUSY WZW models, these algebraic structures are reduced to Lie bialgebraic structures as for the N = (2, 2) SUSY WZW case; with the difference that there is a one 2-cocycle for the N = (4, 4) case and there are two 2-cocycles for the N = (8, 8) case. In general, we show that N = (8, 8) SUSY structure on Lie algebra must be constructed from two N = (4, 4) SUSY structures and in special there must be two 2-cocycles for Manin triples (one 2-cocycle for each of the N = (4, 4) structures). Some examples are investigated. In this way, a calculational method for classifying the N = (4, 4) and N = (8, 8) structures on Lie algebras and Lie groups are obtained.

Using the concept of 3-Lie bialgebra, which has recently been defined in arXiv:1604.04475, we construct Bagger-Lambert-Gustavson (BLG) model for M2-brane on Manin triple of a special 3-Lie bialgebra. Then by using of correspondence 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, its algebraic structure is a Lie bialgebra with one 2-cocycle. In this manner by using correspondence of 3-Lie bialgebra and Lie bialgebra (for this special 3-Lie algebra) one can construct M2-brane from a D2-brane and vice versa.