Toward quantized Picard-Vessiot theory, Further observations on our previous example

2013/12/17 by Katsunori Saito, Saito, Katsunori, Hiroshi Umemura +1
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #math.QA

paper · pdf · doi:10.48550/arxiv.1312.4682

arxiv created 2013/12/17 · arxiv updated 2013/12/18

Abstract

It is quite natural to wonder whether there is a difference-differential equations, the Galois group of which is a quantum group that is neither commutative nor co-commutative. Believing that there was no such linear equations, we explored non-linear equations and discovered a such equation. We show that the example is related with a linear equation. We treat only one charming example. It is not, however, an isolated example. We open a window that allows us to have a look at a quantized Picard-Vessiot theory.

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