Nilradicals of Einstein solvmanifolds

Details Nilradicals of Einstein solvmanifolds Nilradicals of Einstein solvmanifolds

2006-12-05

arxiv.org/abs/math/0612117v1

Mathematics

Differential Geometry

22 pages

Scientific paper

A Riemannian Einstein solvmanifold is called standard, if the orthogonal complement to the nilradical of its Lie algebra is abelian. No examples of nonstandard solvmanifolds are known. We show that the standardness of an Einstein metric solvable Lie algebra is completely detected by its nilradical and prove that many classes of nilpotent Lie algebras (Einstein nilradicals, algebras with less than four generators, free Lie algebras, some classes of two-step nilpotent ones) contain no nilradicals of nonstandard Einstein metric solvable Lie algebras. We also prove that there are no nonstandard Einstein metric solvable Lie algebras of dimension less than ten.

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