Author: zskoda Format: TextIt is not stated if the algebra is over reals or complexes. The conventional wisdom is that one considers semisimple Lie algebra over complexes, and then puts an involution on them to create its "real form". (Probably at that stage you take the invariant part and this is over reals and that is the one you talk about?) Among the forms there are compact forms. Now this is a bit different organization, so it should be made precise, I am not sure how in the present form.
It is not stated if the algebra is over reals or complexes. The conventional wisdom is that one considers semisimple Lie algebra over complexes, and then puts an involution on them to create its "real form". (Probably at that stage you take the invariant part and this is over reals and that is the one you talk about?) Among the forms there are compact forms. Now this is a bit different organization, so it should be made precise, I am not sure how in the present form.