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arXiv · 1301.0092

Unipotent differential algebraic groups as parameterized differential Galois groups

Andrey Minchenko·Alexey Ovchinnikov·Michael F. Singer
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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.

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BibTeXRIS

Andrey Minchenko, Alexey Ovchinnikov, Michael F. Singer. 2013-07-04. Unipotent differential algebraic groups as parameterized differential Galois groups. https://doi.org/10.1017/s1474748013000200

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