Unipotent differential algebraic groups as parameterized differential Galois groups
2013 ◽
Vol 13
(4)
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pp. 671-700
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Keyword(s):
AbstractWe deal with aspects of 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 $0$.
2018 ◽
Vol 20
(04)
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pp. 1750038
Keyword(s):
2014 ◽
Vol 142
(4)
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pp. 1193-1207
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Keyword(s):
2014 ◽
Vol 57
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pp. 44-59
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2001 ◽
Vol 11
(6)
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pp. 489-536
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Keyword(s):
2016 ◽
Vol 75
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pp. 25-55
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