Einstein solvmanifolds with free nilradical

Details Einstein solvmanifolds with free nilradical Einstein solvmanifolds with free nilradical

2006-09-30

arxiv.org/abs/math/0610020v3

Mathematics

Differential Geometry

14 pages, changes to introduction, one reference added, small changes to the text and to the title

Scientific paper

We classify solvable Lie groups with a free nilradical admitting an Einstein left-invariant metric. Any such group is essentially determined by the nilradical of its Lie algebra, which is then called an Einstein nilradical. We show that among the free Lie algebras, there are very few Einstein nilradicals. Except for the one-step (abelian) and the two-step ones, there are only six others: f(2,3), f(2,4), f(2,5), f(3,3), f(4,3), f(5,3) (where f(m,p) is a free p-step Lie algebra on m generators). The reason for that is the inequality-type restrictions on the eigenvalue type of an Einstein nilradical obtained in the paper.

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