Geodesic
On non-standard Einstein extensions of five dimensional nilpotent metric Lie algebras
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 3 (2006), pp. 115-136

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Non-standard Einstein extensions of five-dimensional nilpotent metric Lie algebras are studied in the article. The main result is the following: if there exists a non-standard Einstein extension of a given five-dimensional nilpotent metric Lie algebra $(\frak{n},Q)$, then $\frak{n}$ has the following non-trivial bracket relations: $[X_1,X_2]=X_3$, $[X_1,X_4]=X_5,\,[X_2,X_3]=X_5$ in a basis $\{X_1, X_2, X_3,X_4,X_5\}$. 
@article{SEMR_2006_3_a5,
     author = {E. V. Nikitenko},
     title = {On non-standard {Einstein} extensions of five dimensional nilpotent metric {Lie} algebras},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {115--136},
     publisher = {mathdoc},
     volume = {3},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2006_3_a5/}
}
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E. V. Nikitenko. On non-standard Einstein extensions of five dimensional nilpotent metric Lie algebras. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 3 (2006), pp. 115-136. http://geodesic.mathdoc.fr/item/SEMR_2006_3_a5/