References for Lie algebra extensions, Poincaré

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I will be posting this to the physics stack since this is a physics paper, but I figured the mathematicians would be able to suggest more comprehensive references for me.

My future adviser just published a beautiful paper, https://arxiv.org/pdf/1904.08304.pdf, and I am looking for some references/textbooks to look into the following concepts:

  • Lie algebra (central) extensions
  • Poincaré algebra
  • Galilean algebra
  • Maurer–Cartan forms

Thank you! Cheers