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Journal of Noncommutative Geometry


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Volume 3, Issue 1, 2009, pp. 125–149
DOI: 10.4171/JNCG/33

Published online: 2009-03-31

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

Lucia Di Vizio[1]

(1) Institut de Mathématiques de Jussieu

In this article, 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–Vologodsky and by Baranovsky–Ginzburg.

Keywords: q-difference equations, analytic classification, small divisors, |q| = 1

Di Vizio Lucia: Local analytic classification of q-difference equations with |q| = 1. J. Noncommut. Geom. 3 (2009), 125-149. doi: 10.4171/JNCG/33