- #1

- 343

- 11

## Main Question or Discussion Point

When do we call a representation complex? What are examples of complex representations?

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

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