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
Datum:2020
Hauptverfasser: Grabowska, Katarzyna, Grabowski, Janusz
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2020
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
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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.
first_indexed 2026-04-17T20:23:18Z
format Article
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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.
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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