In my limited study of abstract Lie groups, I have come across the adjoint representation ##Ad: G \to GL(\mathfrak{g})## on the lie algebra ##\matfrak{g}##. It is defined through the conjugation map ##C_g(h) = ghg^{-1}## as the pushforward ##C_{g*}|_{g=e}: \mathfrak{g} \to \mathfrak{g}##.(adsbygoogle = window.adsbygoogle || []).push({});

Does this bear any relation to that one would call the adjoint of a matrix? I.e. the operation where one transposes and takes the complex conjugate?

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# Adjoint representation vs the adjoint of a matrix

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