Realizations of real low-dimensional Lie algebras

@article{Popovych2003RealizationsOR,
  title={Realizations of real low-dimensional Lie algebras},
  author={R. Popovych and V. M. Boyko and M. Nesterenko and Maxim W. Lutfullin},
  journal={Journal of Physics A},
  year={2003},
  volume={36},
  pages={7337-7360}
}
  • R. Popovych, V. M. Boyko, +1 author Maxim W. Lutfullin
  • Published 2003
  • Mathematics, Physics
  • Journal of Physics A
  • 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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    References

    SHOWING 1-10 OF 132 REFERENCES
    Structure of real Lie algebras
    • 30
    Classification of Solvable Lie Algebras
    • W. Graaf
    • Mathematics, Computer Science
    • Exp. Math.
    • 2005
    • 72
    • PDF
    7-dimensional nilpotent Lie algebras
    • 71
    • PDF
    Subalgebras of real three‐ and four‐dimensional Lie algebras
    • 243
    CLASSIFICATION OF NILPOTENT LIE ALGEBRAS OF DIMENSION EIGHT
    • 12
    PRODUCT STRUCTURES ON FOUR DIMENSIONAL SOLVABLE LIE ALGEBRAS
    • 77
    • PDF
    A construction of transitively differential groups of degree 3
    • 4