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

Non-Abelian discrete Toda chains and related lattices