Difference Galois theory of linear differential equations

2013/02/28 by Di Vizio, Lucia, Hardouin, Charlotte, Wibmer, Michael · 2 citations
#12F10 #12H05 #12H10 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #Dynamical Systems (math.DS) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1302.7198

Abstract

We develop a Galois theory for linear differential equations equipped with the action of an endomorphism. This theory is aimed at studying the difference algebraic relations among the solutions of a linear differential equation. The Galois groups here are linear difference algebraic groups, i.e., matrix groups defined by algebraic difference equations.

Cited by

• Dimension Polynomials for Affine Partial Difference Algebraic Groups
• Trivializing Torsors for Difference Algebraic Groups

Related

• Algebraic groups as difference Galois groups of linear differential equations
• Galois Groups of Linear Difference-Differential Equations
• On the Computation of the Galois Group of Linear Difference Equations
• Galois Theory of Parameterized Differential Equations and Linear Differential Algebraic Groups
• On the Definitions of Difference Galois Groups