On derivations of subalgebras of real semisimple Lie algebras

2016/06/17 by Ciatti, Paolo, Cowling, Michael · 1 citation
#17B40 #22E60 #30L10 #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1606.05620

Abstract

Let \mathfrakg be a real semisimple Lie algebra with Iwasawa decomposition \mathfrakk ⊕ \mathfraka ⊕ \mathfrakn. We show that, except for some explicit exceptional cases, every derivation of the nilpotent subalgebra \mathfrakn that preserves its restricted root space decomposition is of the form ad( W), where W ∈ \mathfrakm⊕ .

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