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I hope it's not the wrong forum for my question which is the following:

Is there some list of Lie algebras, whose adjoint representations have the same dimension as their basic representation (like, e.g., this is the case for so(3))? How can one find such Lie algebras? Could you recommend some literature to me?

Thanks in advance!

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# Adjoint representation of a Lie algebra of a same dimension that the basis representa

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