Where can I find a proof that complex representations of a real Lie algebra is equivalent to complex representations of its complexification

Asked May 09 '25 at 10:54

Active May 09 '25 at 10:54

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I have read in a few places, including on this site, that the category of complex representations of a real Lie algebra is equivalent to the category of complex representations of its complexification. Where can I find a proof?

asked May 09 '25 at 10:54

Mozibur Ullah

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But at the site you have linked here, there is an answer by Qiaochu Yuan, right? It follows directly from the universal property of complexification, if I understood correctly. – Dietrich Burde May 09 '25 at 11:01
@Dietrich Burde: Ah yes - I hadn't understood the proof at first, but I get it now. – Mozibur Ullah May 09 '25 at 12:17

Where can I find a proof that complex representations of a real Lie algebra is equivalent to complex representations of its complexification

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