Abstract
On noncommutative spaces, integrable hierarchies of hydrodynamic type systems (1\(^{st}\)-order quasilinear PDE’s) do not, in general, exist. Nevertheless, an infinite-component hydrodynamic chain defined below is shown to be integrable. Its modified version is also constructed and it exhibits a new purely noncommutative phenomenon: the number of modified variables is either \(2\) or \(\infty\).
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