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 .

arXiv comment29 pages