It is the unique Cartan involution of\\ mathfrak if and only if the Killing form of\\ mathfrak is negative definite or, equivalently, if and only if\\ mathfrak is the Lie algebra of a compact semisimple Lie group.
It is the unique Cartan involution of\\ mathfrak if and only if the Killing form of\\ mathfrak is negative definite or if and only if\\ mathfrak is the Lie algebra of a compact semisimple Lie group. This is equivalently.