Year: 2014
Type: article
Abstract: We develop a Galois theory for systems of linear difference equations with an action of an endomorphism σ .This provides a technique to test whether solutions of such systems satisfy σ -polynomial equations and, if yes, then characterize those.We also show how to apply our work to study isomonodromic difference equations and difference algebraic properties of meromorphic functions.1 Introduction Inspired by the numerous applications of the differential algebraic independence results from [36], we develop a Galois theory with an action of an endomorphism σ for systems of linear difference equations of the form φ(y) = Ay, where A ∈ GL n (K) and K is a φσfield, that is, a field with two given commuting endomorphisms φ and σ , such as in Example 2.1.This provides a technique to test whether solutions of such systems satisfy σ -polynomial equations and, if yes, then characterize those.Galois groups, in this approach, are groups of invertible matrices defined by σ -polynomial equations with coefficients in the σ -field K φ := {a ∈ K | φ(a) = a}.In more technical terms, such groups are functors from K φ -σ -algebras to sets represented by finitely σ -generated K φ -σ -Hopf
DOI: 10.1093/imrn/rnu060
Authors: A. Ovchinnikov, M. Wibmer
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2159676403