Poincaré group and the Bargmann theorem

Question

In Valter Moretti's book (Spectral Theory and Quantum Mechanics), page 578, it is said that the Poincaré group is semisimple, but Wikipedia says otherwise.
Moretti mentions it in order to ensure that the Poincaré group satisfies the assumptions of the Bargmann theorem.
Is there something I am missing? Is Moretti committing a mistake? Are there several Poincaré groups, only some of which are semisimple? Do they all have vanishing degree $2$ cohomology (the essential condition in Barmann's theorem)?

Valter Moretti · Accepted Answer

Yes, indeed that statement has been already corrected in the second edition of my book. Poincare group is a semi direct product of $SL(2,C)$ and the abelian Lie group $R^4$. The former is a (semi) simple Lie group, this is enough for extending the thesis of Bargmann’s theorem. The proof appears already in Bargmann’s paper.

Correct answer by Valter Moretti on April 25, 2021

Poincaré group and the Bargmann theorem

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