When do we call a representation complex? What are examples of complex representations?(adsbygoogle = window.adsbygoogle || []).push({});

Also, when we say real and complex forms of Lie algebras, is that related to real and complex representation classification?

I read that spinors are complex representations of SO(3), because their components are complex and the matrices that act on them have complex entries. But then I read elswhere SU(n) with comlex entries, but taken over the real numbers is a real form.

Or does it come down to structure constants? If they are real or complex, so is the representation?

THANKS

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# Complex representation

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