Abstract
This paper provides a new representation of sl(3;ℂ), i.e., a high-dimensional special linear Lie algebra A, which contributes to the generation of a series of simple Lie algebras owning different bases with inequable commutators. Their counterparts are obtained in succession by using some special invertible linear transformations. As applications, the quasi-AKNS and quasi-so(3) type AKNS Hamiltonian hierarchies as well as their nonlinear continuous integrable couplings with the Hamiltonian structures are established, respectively.
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