  Deformations of the structure constants for a class of associative
noncommutative algebras generated by Deformation Driving Algebras (DDA's) are
defined and studied. These deformations are governed by the Central System
(CS). Such a CS is studied for the case of DDA being the algebra of shifts.
Concrete examples of deformations for the three-dimensional algebra governed by
discrete and mixed continuous-discrete Boussinesq (BSQ) and WDVV equations are
presented. It is shown that the theory of the Darboux transformations, at least
for the BSQ case, is completely incorporated into the proposed scheme of
deformations.
