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I am looking for some worked examples of questions like "Compute the root system of the special orthognal Lie algebra $\mathfrak{so}_{2n}$". I understand the theory but find the computations quite fiddly, and I'd like to see the most efficient approaches in order to optimise my own solutions.

Could anyone point me to some lecture notes or slides (or whatever) with examples of this? Thanks!

N.b. I am preparing for an exam where questions of this form are likely to be asked, so I need to be able to compute the root system quickly and correctly.

Sebastian Monnet
  • 3,979
  • This depends on how much theory is known and can be used. A computation from scratch might be (not hard, but) quite long, compare e.g. the answers to https://math.stackexchange.com/q/3768129/96384 and links therein, so I have a hard time imagining that as an exam question. (To be fair, there we compute the root spaces, not just the roots, but even that would need a moment. I mean, you first have to choose a Cartan subalgebra; I would always assume one at least knows the roots and root spaces in $\mathfrak{sl}_n$ and embeds into that, etc.) – Torsten Schoeneberg Mar 07 '21 at 05:45

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