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# classificationClassification of real forms byupto inner automorphisms

I hope to know the classification of real forms of complex simple Lie algebras of types A, D, E $A$, $D$, $E$ up to inner automorphisms.

Let g_1 $\mathfrak{g}_1$ and g_2 $\mathfrak{g}_2$ be real forms of a complex simple Lie algebra g. $\mathfrak{g}$. We say that they are equivalent if there is an isomorphism g_1 ---> g_2 $\mathfrak{g}_1 \to \mathfrak{g}_2$ which extends to an inner automorphism of g. This $\mathfrak{g}$. However, there may result in be real forms which are isomorphic but not equivalent.

Where can we find the classification of such equivalence classes of real forms?

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# classification of real forms by inner automorphisms

I hope to know the classification of real forms of complex simple Lie algebras of types A, D, E up to inner automorphisms. Let g_1 and g_2 be real forms of a complex simple Lie algebra g. We say that they are equivalent if there is an isomorphism g_1 ---> g_2 which extends to an inner automorphism of g. This may result in real forms which are isomorphic but not equivalent. Where can we find the classification of such equivalence classes of real forms?