# Einstein solvmanifolds with a simple Einstein derivation

@article{Nikolayevsky2007EinsteinSW,
title={Einstein solvmanifolds with a simple Einstein derivation},
author={Yuri Nikolayevsky},
journal={Geometriae Dedicata},
year={2007},
volume={135},
pages={87-102}
}
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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