Algebraic groups as difference Galois groups of linear differential equations

Annette Bachmayr, Michael Wibmer*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Article number106854
JournalJournal of Pure and Applied Algebra
Issue number2
Publication statusPublished - Feb 2022


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

ASJC Scopus subject areas

  • Algebra and Number Theory


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