6533b852fe1ef96bd12ab8a5

RESEARCH PRODUCT

Algebraic groups as difference Galois groups of linear differential equations

Annette BachmayrMichael Wibmer

subject

Linear algebraic groupPure mathematicsAlgebra and Number TheoryEndomorphism010102 general mathematicsGalois theoryGalois groupField (mathematics)Commutative Algebra (math.AC)Mathematics - Commutative Algebra01 natural sciencesMathematics - Algebraic GeometryLinear differential equationAlgebraic group0103 physical sciencesFOS: Mathematics010307 mathematical physics0101 mathematicsAlgebraic numberAlgebraic Geometry (math.AG)12H10 12H05 34M15 34M50 14L15Mathematics

description

We study the inverse problem in the difference Galois theory of linear differential equations over the difference-differential field $\mathbb{C}(x)$ with derivation $\frac{d}{dx}$ and endomorphism $f(x)\mapsto f(x+1)$. Our main result is that every linear algebraic group, considered as a difference algebraic group, occurs as the difference Galois group of some linear differential equation over $\mathbb{C}(x)$.

yearjournalcountryeditionlanguage
2019-12-03Journal of Pure and Applied Algebra
https://doi.org/10.1016/j.jpaa.2021.106854