Free differential Galois groups

Algebraic D-groups and Differential Galois Theory

We discuss various relationships between the algebraic Dgroups of Buium, 1992, and differential Galois theory. In the first part we give another exposition of our general differential Galois theory, which is somewhat more explicit than Pillay, 1998, and where generalized logarithmic derivatives on algebraic groups play a central role. In the second part we prove some results with a “constrained...

Free Products of Absolute Galois Groups *

Galois theory, graphs and free groups

A self-contained exposition is given of the topological and Galois-theoretic properties of the category of combinatorial 1-complexes, or graphs, very much in the spirit of Stallings [20]. A number of classical, as well as some new results about free groups are derived.

Around the numeric-symbolic computation of differential Galois groups

Let L∈K(z)[∂] be a linear differential operator, where K is an effective algebraically closed subfield of C. It can be shown that the differential Galois group of L is generated (as a closed algebraic group) by a finite number of monodromy matrices, Stokes matrices and matrices in local exponential groups. Moreover, there exist fast algorithms for the approximation of the entries of these matri...

Galois Theory of Differential Equations, Algebraic Groups and Lie Algebras

As a consequence the level of exposition varies considerably. In particular, some proofs (marked by ¶) and the Appendix require more mathematical background than the main body of the text. The reader is advised to study the paper without paying too much attention to those technical details. This gives sufficient information to complete the exercises. We hope that this introduction might motivat...