Abstract
From a given discrete spectral problem we construct Lax operators for hierarchies of isospectral and nonisospectral lattice soliton systems systematically. We also present algebraic structures of the Kac-Moody-Virasoro type (Witt algebra) related to Lax operators. Based on these algebraic structures we get directly an algebra of commuting symmetry and master symmetry vector fields. Three hierarchies of coupled discrete systems of evolution equations are treated in detail.
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