  In this paper, we establish, under convenient diophantine assumptions, a
complete analytic classification of $q$-difference modules over the field of
germs of meromorphic functions at zero, proving some analytic analogs of the
results by Soibelman and Vologodsky, cf. math.AG/0205117, and by Baranovsky and
Ginzburg, cf. alg-geom/9607008.
