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Symmetry, Integrability and Geometry: Methods and Applications, 2020, Volume 16, 065, 14 pp.
DOI: https://doi.org/10.3842/SIGMA.2020.065 (Mi sigma1602) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Solvable Lie Algebras of Vector Fields and a Lie's Conjecture

Katarzyna Grabowskaa, Janusz Grabowskib

a Faculty of Physics, University of Warsaw, Poland
b Institute of Mathematics, Polish Academy of Sciences, Poland
Full-text PDF (366 kB) Citations (2)
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DOI: https://doi.org/10.3842/SIGMA.2020.065
Abstract: 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 a Lie's conjecture for such Lie algebras. Also infinite-dimensional analytical solvable and transitive Lie algebras of vector fields whose derivative ideal is nilpotent can be adapted to this scheme.
Keywords: vector field, nilpotent Lie algebra, solvable Lie algebra, dilation, foliation.
Funding agency Grant number
Narodowe Centrum Nauki 2016/22/M/ST1/00542
Research founded by the Polish National Science Centre grant under the contract number 2016/22/M/ST1/00542.
Received: February 4, 2020; in final form July 2, 2020; Published online July 10, 2020
Bibliographic databases:
Document Type: Article
MSC: 17B30, 17B66, 57R25, 57S20
Language: English
Citation: Katarzyna Grabowska, Janusz Grabowski, “Solvable Lie Algebras of Vector Fields and a Lie's Conjecture”, SIGMA, 16 (2020), 065, 14 pp.
Citation in format AMSBIB
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    Citing articles in Google Scholar: Russian citations, English citations
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