Algebraic groups as difference Galois groups of linear differential equations.

We study the inverse problem in the difference Galois theory of linear differential equations over the difference-differential field C (x) with derivation d d x 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). [ABSTRACT FROM AUTHOR]