Geodesic
On Einstein Extensions of Nilpotent Metric Lie Algebras
Matematičeskie trudy, Tome 10 (2007) no. 1, pp. 164-190

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The main result of the article is as follows: If a nilpotent noncommutative metric Lie algebra $(\mathfrak n,Q)$ is such that the operator $\operatorname{Id}-\frac{\operatorname{trace}(\mathrm{Ric})}{\operatorname{trace}(\mathrm{Ric}^2)}\mathrm{Ric}$ is positive definite then every Einstein solvable extension of $(\mathfrak n,Q)$ is standard. We deduce several consequences of this assertion. In particular, we prove that all Einstein solvmanifolds of dimension at most 7 are standard. 
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     author = {Yu. G. Nikonorov},
     title = {On {Einstein} {Extensions} of {Nilpotent} {Metric} {Lie} {Algebras}},
     journal = {Matemati\v{c}eskie trudy},
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Yu. G. Nikonorov. On Einstein Extensions of Nilpotent Metric Lie Algebras. Matematičeskie trudy, Tome 10 (2007) no. 1, pp. 164-190. http://geodesic.mathdoc.fr/item/MT_2007_10_1_a7/