Geometriae Dedicata

, Volume 135, Issue 1, pp 87–102 | Cite as

Einstein solvmanifolds with a simple Einstein derivation

  • Yuri Nikolayevsky
Original Paper


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).


Einstein solvmanifold Einstein nilradical Filiform Lie algebra 

Mathematics Subject Classification (2000)

53C30 53C25 


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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of MathematicsLa Trobe UniversityMelbourneAustralia

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