Journal of Noncommutative Geometry, 3(1), 2009, 125--149. 
Abstract:
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.
doi:10.4171/JNCG/33
Arxiv:0802.4223
HAL:hal-00350718