# A curve of nilpotent Lie algebras which are not Einstein nilradicals - Mathematics > Differential Geometry

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Abstract: The only known examples of noncompact Einstein homogeneous spaces arestandard solvmanifolds special solvable Lie groups endowed with a leftinvariant metric, and according to a long standing conjecture, they might beall. The classification of Einstein solvmanifolds is equivalent to the one ofEinstein nilradicals, i.e. nilpotent Lie algebras which are nilradicals of theLie algebras of Einstein solvmanifolds. Up to now, there have been found veryfew examples of graded nilpotent Lie algebras that can not be Einsteinnilradicals. In particular, in each dimension, there are only finitely manyknown. We exhibit in the present paper two curves of pairwise non-isomorphic9-dimensional 2-step nilpotent Lie algebras which are not Einstein nilradicals.

Author: ** Cynthia E. Will**

Source: https://arxiv.org/