# Where to learn about Poincaré Group properties?

I am studying my first QFT course, and there seems to be a lot that I was not taught in previous courses. In my first assignment, I have to prove several properties about the Poincare group, but I have barely any knowledge about them. I looked at the book "Group Theory in a Nutshell for physicists", by A. Zee, but I did not find anything on Poincare transformations. Two examples of the kind of questions I wish to be able to answer are:

1. Determine the inverse and unity element of the Poincare group, as well as the multiplication rule $$(\Lambda_1,a_1)(\Lambda_2,a_2)$$

2. Show that the traslation generators commute, $$[P^{\mu},P^{\nu}]=0$$

What book/paper/resource would be a good place for me to start studying this subject?

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• Try Wu-Ki Tung's Group Theory in Physics. It's basically designed precisely to give this kind of background. – knzhou Aug 31 at 0:45
• The first few chapters of Weinberg's QFT should do the trick. – AccidentalFourierTransform Aug 31 at 0:56
• Poincaré transformations are just Lorentz transformations (Lorentz boosts combined with spatial rotations) combined with spacetime translations. From the Poincaré transformation $x’=\Lambda x+a$ you can figure out the identity element, the inverse, and the composition rule. No book necessary! – G. Smith Aug 31 at 4:19