Calculating the Galois group of L1(L2(y))=0,L1,L2 completely reducible operators

Calculating the Galois Group of L 1 (l 2 (y)) = 0, L 1 ; L 2 Completely Reducible Operators

Calculating the Galois Group of Y'= = = AY+ + + B, Y'= = = AY Completely Reducible

We consider a special case of the problem of computing the Galois group of a system of linear ordinary differential equations Y ′ = MY, M ∈ C(x)n×n. We assume that C is a computable, characteristic-zero, algebraically closed constant field with factorization algorithm. There exists a decision procedure, due to Compoint and Singer, to compute the group in case the system is completely reducible....

Computing Galois Groups of Completely Reducible Differential Equations

At present we do not know a general algorithm that will compute the Galois group of a linear differential equation with coefficients in a differential field k, even when k = Q̄(x), where Q̄ is the algebraic closure of the rational numbers. In contrast, algorithms for calculating the Galois group of a polynomial with coefficients in Q or Q̄(x) have been known for a long time (van der Waerden, 1953;...

Completely reducible sets

We study the family of rational sets of words, called completely reducible and which are such that the syntactic representation of their characteristic series is completely reducible. This family contains, by a result of Reutenauer, the submonoids generated by bifix codes and, by a result of Berstel and Reutenauer, the cyclic sets. We study the closure properties of this family. We prove a resu...

Completely Reducible Lie Subalgebras

Let G be a connected and reductive group over the algebraically closed field K. J-P. Serre has introduced the notion of a G-completely reducible subgroup H ≤ G. In this note, we give a notion of G-complete reducibility – G-cr for short – for Lie subalgebras of Lie(G), and we show that if the smooth subgroup H < G is G-cr, then Lie(H) is G-cr as well.