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

Symmetry Integrability and Geometry-Methods and Applications

article

Katarzyna Grabowska¹  Janusz Grabowski² 

[1] Faculty of Physics, University of Warsaw;Institute of Mathematics, Polish Academy of Sciences

关键词: vector field;    nilpotent Lie algebra;    solvable Lie algebra;    dilation;    foliation;   

DOI  :  10.3842/SIGMA.2020.065

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown