Complex matrix Lie algebra

Keppeler's matrix Lie algebra convention

In his course Groups and Representations, Stefan Keppeler uses a slightly unorthodox convention of multiplying tangential matrices by when forming the Complex matrix Lie algebra¹, so given a Lie group

Then the Lie bracket becomes the matrix commutator premultiplied by . When used in these notes, I will reserve the brackets for the commutator and explicitly prepend the .

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