Almost inner derivations of Lie algebras
Dietrich BurdeFakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, 1090 Wien, AustriaKarel DekimpeKatholieke Universiteit Leuven Kulak, E. Sabbelaan, 53 Bus 7657, 8500 Kortrijk, BelgiumBert VerbekeKatholieke Universiteit Leuven Kulak, E. Sabbelaan, 53 Bus 7657, 8500 Kortrijk, Belgium
2017en
ABI
Abstract
We study almost inner derivations of Lie algebras, which were introduced by Gordon and Wilson in their work on isospectral deformations of compact solvmanifolds. We compute all almost inner derivations for low-dimensional Lie algebras, and introduce the concept of fixed basis vectors for proving that all almost inner derivations are inner for [Formula: see text]-step nilpotent Lie algebras determined by graphs, free [Formula: see text] and [Formula: see text]-step nilpotent Lie algebras, free metabelian nilpotent Lie algebras on two generators, almost abelian Lie algebras and triangular Lie algebras. On the other hand, we also exhibit families of nilpotent Lie algebras having an arbitrary large space of non-inner almost inner derivations.
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Cited by 20 references