Abstract
In the paper, a super-discrete variational identity on Lie super-algebras is established first. It provides an approach for constructing super-discrete Hamiltonian structures of super evolution lattice equations with discrete zero curvature representation when the super-spectral matrix U is selected appropriately. As an application, super-discrete Hamiltonian structures of super-Toda lattice hierarchy are developed and this method can be used to construct super-discrete bi-Hamiltonian structures of more super-discrete integrable evolutive hierarchies. Super-discrete variational identity is devoted to deduce super-integrability and solutions of super-discrete integrable equations.
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