Geodesic
Einstein Solvmanifolds and Two-Step Nilpotent Lie Algebras with a Special Nice Basis
Journal of Lie theory, Tome 28 (2018) no. 2, pp. 343-356 Cet article a éte moissonné depuis la source Heldermann Verlag

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Consider a two-step nilpotent Lie algebra n with a special nice basis as introduced by Y. Nikolayevsky [Einstein solvmanifolds and the pre-Einstein derivation, Trans. Amer. Math. Soc. 363 (2011) 3935--3958] endowed with an inner product which makes the basis orthonormal. We describe necessary and sufficient conditions for the existence of a rank-one Einstein metric solvable extension of n. Since every two-step nilpotent Lie algebra attached to a graph (as introduced by S. G. Dani, M. G. Mainkar [Anosov automorphisms on compact nilmanifolds associated with graphs, Trans. Amer. Math. Soc. 357 (2005) 2235--2251]) has such a nice basis, this note generalizes a recent result of H.-R. Fanaï [Einstein solvmanifolds and graphs, C. R. Acad. Sci. Paris, Ser. I 344 (2007) 37--39].
Classification : 22E60, 53C25
Mots-clés : Nice basis, two-step nilpotent Lie algebra, Einstein solvmanifolds 
@article{JLT_2018_28_2_JLT_2018_28_2_a2,
     author = {H.-R. Fana{\"\i} and Z. Khodaei},
     title = {Einstein {Solvmanifolds} and {Two-Step} {Nilpotent} {Lie} {Algebras} with a {Special} {Nice} {Basis}},
     journal = {Journal of Lie theory},
     pages = {343--356},
     year = {2018},
     volume = {28},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JLT_2018_28_2_JLT_2018_28_2_a2/}
}
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H.-R. Fanaï; Z. Khodaei. Einstein Solvmanifolds and Two-Step Nilpotent Lie Algebras with a Special Nice Basis. Journal of Lie theory, Tome 28 (2018) no. 2, pp. 343-356. http://geodesic.mathdoc.fr/item/JLT_2018_28_2_JLT_2018_28_2_a2/