We recently introduced a class of ##IMG## [http://ej.iop.org/images/1751-8121/53/23/235201/aab8b36ieqn2.gif] {${\mathbb{Z}}_{N}$} graded discrete Lax pairs and studied the associated discrete integrable systems (lattice equations). We discuss differential–difference equations which then we interpret as symmetries of the discrete systems. In particular, we present nonlocal symmetries which are associated with the 2D Toda lattice.

中文翻译：

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## IMG ##的对称性[http://ej.iop.org/images/1751-8121/53/23/235201/toc_aab8b36ieqn1.gif] {$ {\ mathbb {Z}} _ {N} $}分离散可积系统

我们最近推出了一类## IMG ## [http://ej.iop.org/images/1751-8121/53/23/235201/aab8b36ieqn2.gif] {$ {\ mathbb {Z}} _ {N } $}分立离散Lax对，并研究了相关的离散可积系统（晶格方程）。我们讨论了微分差分方程，然后将其解释为离散系统的对称性。特别是，我们提出了与2D Toda晶格相关的非局部对称性。