中文摘要：

在这糊，基于一分离光谱问题并且相应零个弯曲代表， isospectral 和 nonisospectral 格子层次被建议。代数学的结构分离零个弯曲方程然后为如此的 integrable 系统被建立。相应于 isospectral 和 non-isospectral 格子流动的宽松的操作符的交换关系被得出，在 isospectral hierarchyand 的每个格子方程的主人对称被产生，因此，为格子 integrable 系统的对称代数学从这个理论被产生。

英文摘要：

In this paper, based on a discrete spectral problem and the corresponding zero curvature representation,the isospectral and nonisospectral lattice hierarchies are proposed. An algebraic structure of discrete zero curvature equations is then established for such integrable systems. the commutation relations of Lax operators corresponding to the isospectral and non-isospectral lattice flows are worked out, the master symmetries of each lattice equation in the isospectral hierarchyand are generated, thus a τ-symmetry algebra for the lattice integrable systems is engendered from this theory.