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Does anyone know of a classification of those (complex) Lie algebras which are:

  1. generated by two elements
  2. $\mathbb{Z}$-graded Lie algebras
  3. finite dimensional
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    $\begingroup$ There's not even a known classification of 8-dimensional complex Lie algebras graded in positive integers. $\endgroup$
    – YCor
    Commented Dec 7, 2018 at 19:12
  • $\begingroup$ ... and also $\mathbf{Z}$-graded Lie algebras include all Lie algebras $\mathfrak{g}$, graded as $\mathfrak{g}_0$. $\endgroup$
    – YCor
    Commented Dec 7, 2018 at 21:26

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