Realizations of real low-dimensional Lie algebras

@article{Popovych2003RealizationsOR,
  title={Realizations of real low-dimensional Lie algebras},
  author={Roman O. Popovych and Vyacheslav M. Boyko and Maryna Olexandrivna Nesterenko and Maxim W. Lutfullin},
  journal={Journal of Physics A},
  year={2003},
  volume={36},
  pages={7337-7360}
}
Using a new powerful technique based on the notion of megaideal, we construct a complete set of inequivalent realizations of real Lie algebras of dimension no greater than four in vector fields on a space of an arbitrary (finite) number of variables. Our classification amends and essentially generalizes earlier works on the subject. 

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