Mathematische Zeitschrift

, Volume 272, Issue 1–2, pp 675–695 | Cite as

Einstein solvmanifolds attached to two-step nilradicals

  • Yuri NikolayevskyEmail author


A Riemannian Einstein solvmanifold (possibly, any noncompact homogeneous Einstein space) is almost completely determined by the nilradical of its Lie algebra. A nilpotent Lie algebra which can serve as the nilradical of an Einstein metric solvable Lie algebra is called an Einstein nilradical. We give a classification of two-step nilpotent Einstein nilradicals with two-dimensional center. Informally, the defining matrix pencil must have no nilpotent blocks in the canonical form and no elementary divisors of a very high multiplicity. We also show that the dual to a two-step Einstein nilradical is not in general an Einstein nilradical.


Einstein solvmanifold Einstein nilradical Two-step nilpotent Lie algebra 

Mathematics Subject Classification (2000)

53C30 53C25 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsLa Trobe UniversityMelbourneAustralia

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