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Einstein solvmanifolds with a simple Einstein derivation. (English) Zbl 1145.53040
Summary: 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).
MSC:
53C30Homogeneous manifolds (differential geometry)
53C25Special Riemannian manifolds (Einstein, Sasakian, etc.)
17B30Solvable, nilpotent Lie (super)algebras
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