Lie Groups and Lie Algebras using Wolfram Language?

Questions
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1

Sorry if this is repetition, I am fairly new to Mathematica, and would like to use it for the above module, could someone point me in the right direction please… I have used Maple for the differential geometry stuff but lost on Mathematica. I have mainly used Mathematica for Groebner Basis, matrices, complex analysis etc no problem at all.

2

IMHO Lie Groups and Algebras are not built-in into Mathematica, here is a glimpse from the internet

I’ve no experience neither with SAGE nor with LieART.

3

Thanks, I also came across that from Google, I tried a few things but it isn’t really the best. So will use Maple for now until Mathematica polish their lie algebras code.