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My future adviser just published a beautiful paper, https://arxiv.org/abs/1904.08304, 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
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  • $\begingroup$ For some brief notes on the maurer cartan form read the relevant parts of lecture 1 "Connections on principal fibre bundles" from this web page empg.maths.ed.ac.uk/Activities/GT $\endgroup$
    – user1379857
    Commented Apr 20, 2019 at 19:36
  • $\begingroup$ Would Mathematics be a better home for this question? $\endgroup$
    – Qmechanic ♦
    Commented Apr 20, 2019 at 19:58
  • $\begingroup$ @Qmechanic I asked there as well, but being as I'm a physicist, just one who wants to foster a greater degree of communication between mathematics and physics, I thought it appropriate to post in the physics stack as well. $\endgroup$
    – Lopey Tall
    Commented Apr 21, 2019 at 16:53
  • $\begingroup$ Crossposted from math.stackexchange.com/q/3194902/11127 $\endgroup$
    – Qmechanic ♦
    Commented Apr 21, 2019 at 16:55

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You might find the book "Lie Groups, Lie Algebras, Cohomology and some Applications in Physics" by de Azcárraga and Izquierdo covers most of the topics (as you can easily see by looking at the Index).

It is mathematically rigorous but geared towards physical applications and does not need a lot of prerequisites. That it is written by one of the authors of the paper you mention might be an additional benefit.

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  • $\begingroup$ This is a brilliant field! Thank you so much! $\endgroup$
    – Lopey Tall
    Commented Apr 21, 2019 at 20:54

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