Einstein solvmanifolds with a simple Einstein derivation

Details Einstein solvmanifolds with a simple Einstein derivation Einstein solvmanifolds with a simple Einstein derivation

2007-07-31

arxiv.org/abs/0707.4595v1

Mathematics

Differential Geometry

11 pages

Scientific paper

The structure of a solvable Lie groups 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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