Non-Abelian discrete Toda chains and related lattices

Abstract

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 $\to$ Somos-$N$ sequences $\to$ discrete Painlevé equations.

arXiv commentAcknowledgements have been updated. This version of the manuscript corresponds to the journal version

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