Galois groups of linear difference-differential equations

Lie symmetries and differential Galois groups of linear equations

For a linear ordinary differential equation the Lie algebra of its infinitesimal Lie symmetries is compared with its differential Galois group. For this purpose an algebraic formulation of Lie symmetries is developed. It turns out that there is no direct relation between the two above objects. In connection with this a new algorithm for computing the Lie symmetries of a linear ordinary differen...

Galois Groups of Second and Third Order Linear Differential Equations

Using the representation theory of groups, we are able to give simple necessary and suucient conditions regarding the structure of the galois groups of second and third order linear diierential equations. These allow us to give simple necessary and suucient conditions for a second order linear diierential equation to have liouvillian solutions and for a third order linear diierential equation t...

σ-Galois theory of linear difference equations

Inspired by the numerous applications of the differential algebraic independence results from [36], we develop a Galois theory with an action of an endomorphism σ for systems of linear difference equations of the form φ(y) = Ay , where A ∈ GLn(K ) and K is a φσ-field, that is, a field with two given commuting endomorphisms φ and σ, like in Example 2.1. This provides a technique to test whether ...

Galois Theory of Linear Differential Equations

Galois Theory of Linear Differential Equations - ReadingSample