Abstract
The structure of a solvable Lie group admitting an Einstein left-invariant metric is, in a sense, completely determined by the nilradical of its Lie algebra. We give an easy-to-check necessary and sufficient condition for a nilpotent algebra to be an Einstein nilradical whose Einstein derivation has simple eigenvalues. As an application, we classify filiform Einstein nilradicals (modulo known classification results on filiform graded Lie algebras).
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Nikolayevsky, Y. Einstein solvmanifolds with a simple Einstein derivation. Geom Dedicata 135, 87–102 (2008). https://doi.org/10.1007/s10711-008-9264-y
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DOI: https://doi.org/10.1007/s10711-008-9264-y