Reduced Forms of Linear Differential Systems and the Intrinsic Galois-Lie Algebra of Katz
Generalizing the main result of [Aparicio-Monforte A., Compoint E., Weil J.-A., J. Pure Appl. Algebra 217 (2013), 1504-1516], we prove that a linear differential system is in reduced form in the sense of Kolchin and Kovacic if and only if any differential module in an algebraic construction admits a...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2020 |
| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210696 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Reduced Forms of Linear Differential Systems and the Intrinsic Galois-Lie Algebra of Katz. Moulay Barkatou, Thomas Cluzeau, Lucia Di Vizio and Jacques-Arthur Weil. SIGMA 16 (2020), 054, 13 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | Generalizing the main result of [Aparicio-Monforte A., Compoint E., Weil J.-A., J. Pure Appl. Algebra 217 (2013), 1504-1516], we prove that a linear differential system is in reduced form in the sense of Kolchin and Kovacic if and only if any differential module in an algebraic construction admits a constant basis. Then we derive an explicit version of this statement. We finally deduce some properties of the Lie algebra of Katz's intrinsic Galois group.
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| ISSN: | 1815-0659 |