Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 16 (2020), 065, 14 pages      arXiv:1907.02925      https://doi.org/10.3842/SIGMA.2020.065

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

Katarzyna Grabowska a and Janusz Grabowski b
a) Faculty of Physics, University of Warsaw, Poland
b) Institute of Mathematics, Polish Academy of Sciences, Poland

Received February 04, 2020, in final form July 02, 2020; Published online July 10, 2020

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.

Key words: vector field; nilpotent Lie algebra; solvable Lie algebra; dilation; foliation.

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