We use quantum tori Lie algebras (QTLA), which are a one-parameter fam
ily of sub-algebras of gl(infinity), to describe local and non-local v
ersions of the Toda systems. It turns out that the central charge of Q
TLA is responsible for the non-locality. There are two regimes in the
local systems - conformal for irrational values of the parameter and n
on-conformal and integrable for its rational values. We also consider
infinite-dimensional analogs of rigid tops. Some of these systems give
rise to ''quantized'' (magneto-)hydrodynamic equations of an ideal fl
uid on a torus. We also consider infinite dimensional versions of the
integrable Euler and Clebsch cases.