Unipotent differential algebraic groups as parameterized differential Galois groups
Commutative Algebra
2019-02-20 v2 Classical Analysis and ODEs
Dynamical Systems
Group Theory
Abstract
We deal with aspects of the direct and inverse problems in parameterized Picard-Vessiot (PPV) theory. It is known that, for certain fields, a linear differential algebraic group (LDAG) G is a PPV Galois group over these fields if and only if G contains a Kolchin-dense finitely generated group. We show that, for a class of LDAGs G, including unipotent groups, G is such a group if and only if it has differential type 0. We give a procedure to determine if a parameterized linear differential equation has a PPV Galois group in this class and show how one can calculate the PPV Galois group of a parameterized linear differential equation if its Galois group has differential type 0.
Keywords
Cite
@article{arxiv.1301.0092,
title = {Unipotent differential algebraic groups as parameterized differential Galois groups},
author = {Andrey Minchenko and Alexey Ovchinnikov and Michael F. Singer},
journal= {arXiv preprint arXiv:1301.0092},
year = {2019}
}
Comments
minor revision