In the article differential-difference (semi-discrete) lattices of hyperbolic type are investigated from the integrability viewpoint. More precisely we concentrate on a method for constructing generalized symmetries. This kind integrable lattices admit two hierarchies of generalized symmetries corresponding to the discrete and continuous independent variables n and x. Symmetries corresponding to the direction of n are constructed in a more or less standard way while when constructing symmetries of the other form we meet a problem of solving a functional equation. We have shown that to handle with this equation one can effectively use the concept of characteristic Lie–Rinehart algebras of semi-discrete models. Based on this observation, we have proposed a classification method for integrable semi-discrete lattices. One of the interesting results of this work is a new example of an integrable equation, which is a semi-discrete analogue of the Tzizeica equation. Such examples were not previously known.

在文章中，从可积性的角度研究了双曲型微分差分（半离散）格。更准确地说，我们专注于构建广义对称性的方法。这种可积格允许对应于离散和连续自变量n和x的广义对称性的两个层次结构。对应于n方向的对称性以或多或少的标准方式构造，而在构造另一种形式的对称性时，我们会遇到求解函数方程的问题。我们已经证明，为了处理这个方程，可以有效地使用半离散模型的特征 Lie-Rinehart 代数的概念。基于这一观察，我们提出了一种可积半离散格的分类方法。这项工作的一个有趣结果是可积方程的一个新例子，它是 Tzizeica 方程的半离散模拟。这样的例子以前是未知的。