Abstract
With the exception of the three step real free Lie algebra on two generators, all real free Lie algebras of step at least three are shown to have trivial Tanaka prolongation. This result, together with the known results concerning the step two real free Lie algebras and the step three real free Lie algebra on two generators, gives a complete list of Tanaka prolongations for real free Lie algebras.
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Warhurst, B. Tanaka prolongation of free Lie algebras. Geom Dedicata 130, 59–69 (2007). https://doi.org/10.1007/s10711-007-9205-1
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DOI: https://doi.org/10.1007/s10711-007-9205-1