Cartan Involutions On Lie Algebras
Let be a real semisimple Lie algebra and let be its Killing form. An involution on is a Lie algebra automorphism of whose square is equal to the identity. Such an involution is called a Cartan involution on if is a positive definite bilinear form.
Two involutions and are considered equivalent if they differ only by an inner automorphism.
Any real semisimple Lie algebra has a Cartan involution, and any two Cartan involutions are equivalent.
Read more about this topic: Cartan Decomposition
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