标题： 非阿贝尔离散陶多链和相关格子 显示英文标题

标题： Non-Abelian discrete Toda chains and related lattices

摘要： 我们推导了二维离散Toda格子的非阿贝尔类似物，它以准行列式形式给出解，并且接受不同形式的Lax对。 它与几个著名(1+1)和一维格子的非阿贝尔类似物之间的联系被讨论。 特别是，我们考虑了如下方案的非交换类似物：离散Toda方程$\rightarrow$Somos-$N$序列$\rightarrow$离散Painlevé方程。 显示英文摘要

摘要： We have derived a non-abelian analog for the two-dimensional discrete Toda lattice which possesses solutions in terms of quasideterminants and admits Lax pairs of different forms. Its connection with non-abelian analogs for several well-known (1+1) and one-dimensional lattices is discussed. In particular, we consider a non-commutative analog of the scheme: discrete Toda equations $\rightarrow$ Somos-$N$ sequences $\rightarrow$ discrete Painlev\'e equations.