## Local analytic classification of $q$-difference equations with $|q|=1$

Di Vizio, Lucia
##### Description
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.
Comment: 20 pages. Final version. Improved exposition
##### Keywords
Mathematics - Quantum Algebra, Mathematics - Classical Analysis and ODEs, 39A13, 33E99