Fantappi\`e's final relativity and Lie algebra deformations

The purpose of this note is to discuss a few lines appearing in the work of late Fantappi`e. They concern the proof of rigidity of a specific real semisimple Lie algebra: $\mathfrak{O}(4,1)$. Our intention is to discuss to what extent such proof constitutes a missed opportunity in history of post-war Italian mathematics.