On derivations of subalgebras of real semisimple Lie algebras

Abstract

Let $$\mathfrak {g}$$ be a real semisimple Lie algebra with Iwasawa decomposition $$\mathfrak {k} \oplus \mathfrak {a} \oplus \mathfrak {n}$$ . We show that, except for some explicit exceptional cases, every derivation of the nilpotent subalgebra $$\mathfrak {n}$$ that preserves its restricted root space decomposition is of the form $${\text {ad}}( W)$$ , where $$W \in \mathfrak {m}\oplus \mathfrak {a}$$ .