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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2020 |
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210696 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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 |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862716645924929536 |
|---|---|
| author | Barkatou, Moulay Cluzeau, Thomas Di Vizio, Lucia Weil, Jacques-Arthur |
| author_facet | Barkatou, Moulay Cluzeau, Thomas Di Vizio, Lucia Weil, Jacques-Arthur |
| citation_txt | 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 |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2025-12-17T12:04:31Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210696 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-17T12:04:31Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Barkatou, Moulay Cluzeau, Thomas Di Vizio, Lucia Weil, Jacques-Arthur 2025-12-15T15:22:51Z 2020 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 1815-0659 2020 Mathematics Subject Classification: 34M03; 34M15; 34C20 arXiv:1912.10567 https://nasplib.isofts.kiev.ua/handle/123456789/210696 https://doi.org/10.3842/SIGMA.2020.054 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. We are grateful to the anonymous referees for their relevant suggestions, which helped us to improve the clarity and quality of this work. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Reduced Forms of Linear Differential Systems and the Intrinsic Galois-Lie Algebra of Katz Article published earlier |
| spellingShingle | Reduced Forms of Linear Differential Systems and the Intrinsic Galois-Lie Algebra of Katz Barkatou, Moulay Cluzeau, Thomas Di Vizio, Lucia Weil, Jacques-Arthur |
| title | Reduced Forms of Linear Differential Systems and the Intrinsic Galois-Lie Algebra of Katz |
| title_full | Reduced Forms of Linear Differential Systems and the Intrinsic Galois-Lie Algebra of Katz |
| title_fullStr | Reduced Forms of Linear Differential Systems and the Intrinsic Galois-Lie Algebra of Katz |
| title_full_unstemmed | Reduced Forms of Linear Differential Systems and the Intrinsic Galois-Lie Algebra of Katz |
| title_short | Reduced Forms of Linear Differential Systems and the Intrinsic Galois-Lie Algebra of Katz |
| title_sort | reduced forms of linear differential systems and the intrinsic galois-lie algebra of katz |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210696 |
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