| Abstract: | The only known examples of non-compact Einstein homogeneous spaces are standard solvmanifolds (special solvable Lie groups
endowed with a left invariant metric), and according to a long standing conjecture, they might be all. The classification
of Einstein solvmanifolds is equivalent to the one of Einstein nilradicals, i.e. nilpotent Lie algebras which are nilradicals of the Lie algebras of Einstein solvmanifolds. Up to now, very few examples
of
\mathbb N{\mathbb N}-graded nilpotent Lie algebras that cannot be Einstein nilradicals have been found. In particular, in each dimension, there
are only finitely many known. We exhibit in the present paper two curves of pairwise non-isomorphic nine-dimensional two-step
nilpotent Lie algebras which are not Einstein nilradicals. |
