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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