Algebraic groups as difference Galois groups of linear differential equations

Annette  Bachmayr; Michael Wibmer

doi:10.1016/j.jpaa.2021.106854

Algebraic groups as difference Galois groups of linear differential equations

Annette Bachmayr, Michael Wibmer^*

^*Corresponding author for this work

Institute of Analysis and Number Theory (5010)

Research output: Contribution to journal › Article › peer-review

Abstract

We study the inverse problem in the difference Galois theory of linear differential equations over the difference-differential field C(x) with derivation [Formula presented] and endomorphism f(x)↦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 C(x).

Original language	English
Article number	106854
Journal	Journal of Pure and Applied Algebra
Volume	226
Issue number	2
DOIs	https://doi.org/10.1016/j.jpaa.2021.106854
Publication status	Published - Feb 2022

Keywords

Difference algebraic groups
Differential Galois theory
Inverse problems
Parameterized Picard-Vessiot theory

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jpaa.2021.106854

Cite this

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title = "Algebraic groups as difference Galois groups of linear differential equations",

abstract = "We study the inverse problem in the difference Galois theory of linear differential equations over the difference-differential field C(x) with derivation [Formula presented] and endomorphism f(x)↦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 C(x).",

keywords = "Difference algebraic groups, Differential Galois theory, Inverse problems, Parameterized Picard-Vessiot theory",

author = "Annette Bachmayr and Michael Wibmer",

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AU - Bachmayr, Annette

AU - Wibmer, Michael

PY - 2022/2

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N2 - We study the inverse problem in the difference Galois theory of linear differential equations over the difference-differential field C(x) with derivation [Formula presented] and endomorphism f(x)↦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 C(x).

AB - We study the inverse problem in the difference Galois theory of linear differential equations over the difference-differential field C(x) with derivation [Formula presented] and endomorphism f(x)↦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 C(x).

KW - Difference algebraic groups

KW - Differential Galois theory

KW - Inverse problems

KW - Parameterized Picard-Vessiot theory

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DO - 10.1016/j.jpaa.2021.106854

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JF - Journal of Pure and Applied Algebra

IS - 2

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ER -

Algebraic groups as difference Galois groups of linear differential equations

Abstract

Keywords

ASJC Scopus subject areas

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