Complex sentence: 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.
Split into simpler sentences: It is the unique Cartan involution of\\ mathfrak if and only if the Killing form of\\ mathfrak is negative definite. Equivalently,\\ mathfrak is the Lie algebra of a compact semisimple Lie group.