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arXiv · 1912.01284

Algebraic groups as difference Galois groups of linear differential equations

Annette Bachmayr·Michael Wibmer
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Abstract

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 $\mathbb{C}(x)$.

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Annette Bachmayr, Michael Wibmer. 2019-12-03. Algebraic groups as difference Galois groups of linear differential equations. https://arxiv.org/abs/1912.01284

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