Abstract
A class of new Lie algebra B(3) is constructed, which is far different from the known Lie algebra A(n-1). Based on the corresponding loop algebra (B) over bar (3), the generalized mKdV hierarchy is established. In order to look for the Hamiltonian structure of such integrable system, a generalized trace functional of matrices is introduced, whose special case is just the well-known trace identity. Finally, its expanding integrable model is worked out by use of an enlarged Lie algebra.
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