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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/208446In 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/9607008.20 pages. Final version. Improved expositionQuantum AlgebraClassical Analysis and ODEs39A13, 33E99Local analytic classification of $q$-difference equations with $|q|=1$text