High Quality Content by WIKIPEDIA articles! In mathematics, the notion of a real form relates objects defined over the field of real and complex numbers. A real Lie algebra g0 is called a real form of a complex Lie algebra g if g is the complexification of g0: mathfrak{g}simeqmathfrak{g}_0otimes_{mathbb{R}}mathbb{C}. The notion of a real form can also be defined for complex Lie groups. Real forms of complex semisimple Lie groups and Lie algebras have been completely classified by Elie Cartan.

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