A real form of a complex Lie algebra 
is a real Lie algebra 
whose complexification is isomorphic
to 
. Equivalently, it is the fixed real vector space of a conjugate-linear involutive automorphism
of 
(De Medts 2026).
Being isomorphic to the complex conjugate Lie algebra is necessary but not sufficient. De Medts (2026) constructed a nine-dimensional complex nilpotent Lie algebra of nilpotency class five, generated by two elements, which is isomorphic to its complex conjugate but has no real form. De Medts (2026) acknowledges Claude assistance with constructing and discussing the example.
