#### Conference abstracts

Session B3 - Symbolic Analysis

July 13, 15:30 ~ 15:55 - Room B2

## Computing the Galois-Lie Algebra of Completely Reducible Differential Systems.

### Jacques-Arthur Weil

### Université de Limoges, France - weil@unilim.fr

This talk is related to the work presented by Thomas Dreyfus earlier in this session.\\ A linear differential system $[A]: Y'=AY$ is called completely reducible when $A$ is block-diagonal and each block is the matrix of an irreducible system. We show how to compute the Lie algebra $\mathfrak{g}$ of the Galois group of $[A]$. \\ We will first explain how to represent a copy of $\mathfrak{g}$ as a subsystem of a system constructed on $[A]$. We show how to guess this subsystem by using modular techniques or invariants. Validation of this guess is achieved through, first, computing an explicit conjugacy between Lie algebras and finally finding algebraic solutions of a (small) linear differential system.

Joint work with Moulay Barkatou, Thomas Cluzeau (Université de Limoges, France) and Lucia Di Vizio (Université de Versailles, France).