Solvable Lie Algebras of Vector Fields and a Lie's Conjecture
We present a local and constructive differential geometric description of finite-dimensional solvable and transitive Lie algebras of vector fields. We show that it implies Lie's conjecture for such Lie algebras. Also, infinite-dimensional analytically solvable and transitive Lie algebras of vec...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2020 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2020
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/210783 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Solvable Lie Algebras of Vector Fields and a Lie's Conjecture. Katarzyna Grabowska and Janusz Grabowski. SIGMA 16 (2020), 065, 14 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862750593054932992 |
|---|---|
| author | Grabowska, Katarzyna Grabowski, Janusz |
| author_facet | Grabowska, Katarzyna Grabowski, Janusz |
| citation_txt | Solvable Lie Algebras of Vector Fields and a Lie's Conjecture. Katarzyna Grabowska and Janusz Grabowski. SIGMA 16 (2020), 065, 14 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We present a local and constructive differential geometric description of finite-dimensional solvable and transitive Lie algebras of vector fields. We show that it implies Lie's conjecture for such Lie algebras. Also, infinite-dimensional analytically solvable and transitive Lie algebras of vector fields whose derivative ideal is nilpotent can be adapted to this scheme.
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| first_indexed | 2026-04-17T20:23:18Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210783 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-04-17T20:23:18Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Grabowska, Katarzyna Grabowski, Janusz 2025-12-17T14:38:26Z 2020 Solvable Lie Algebras of Vector Fields and a Lie's Conjecture. Katarzyna Grabowska and Janusz Grabowski. SIGMA 16 (2020), 065, 14 pages 1815-0659 2020 Mathematics Subject Classification: 17B30; 17B66; 57R25; 57S20 arXiv:1907.02925 https://nasplib.isofts.kiev.ua/handle/123456789/210783 https://doi.org/10.3842/SIGMA.2020.065 We present a local and constructive differential geometric description of finite-dimensional solvable and transitive Lie algebras of vector fields. We show that it implies Lie's conjecture for such Lie algebras. Also, infinite-dimensional analytically solvable and transitive Lie algebras of vector fields whose derivative ideal is nilpotent can be adapted to this scheme. We thank the anonymous referees for their careful reading of our manuscript and their insightful comments. Following their suggestions, we included several improvements in the manuscript. Research funded by the Polish National Science Centre grant under the contract number 2016/22/M/ST1/00542. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Solvable Lie Algebras of Vector Fields and a Lie's Conjecture Article published earlier |
| spellingShingle | Solvable Lie Algebras of Vector Fields and a Lie's Conjecture Grabowska, Katarzyna Grabowski, Janusz |
| title | Solvable Lie Algebras of Vector Fields and a Lie's Conjecture |
| title_full | Solvable Lie Algebras of Vector Fields and a Lie's Conjecture |
| title_fullStr | Solvable Lie Algebras of Vector Fields and a Lie's Conjecture |
| title_full_unstemmed | Solvable Lie Algebras of Vector Fields and a Lie's Conjecture |
| title_short | Solvable Lie Algebras of Vector Fields and a Lie's Conjecture |
| title_sort | solvable lie algebras of vector fields and a lie's conjecture |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210783 |
| work_keys_str_mv | AT grabowskakatarzyna solvableliealgebrasofvectorfieldsandaliesconjecture AT grabowskijanusz solvableliealgebrasofvectorfieldsandaliesconjecture |