Einstein solvmanifolds attached to two-step nilradicals
| dc.creator | Nikolayevsky, Y. | |
| dc.date | 2008-05-06 | |
| dc.date.accessioned | 2026-07-07T09:37:14Z | |
| dc.date.available | 2026-07-07T09:37:14Z | |
| dc.description | A Riemannian Einstein solvmanifold (possibly, any noncompact homogeneous Einstein space) is almost completely determined by the nilradical of its Lie algebra. A nilpotent Lie algebra, which can serve as the nilradical of an Einstein metric solvable Lie algebra, is called an Einstein nilradical. Despite a substantial progress towards the understanding of Einstein nilradicals, there is still a lack of classification results even for some well-studied classes of nilpotent Lie algebras, such as the two-step ones. In this paper, we give a classification of two-step nilpotent Einstein nilradicals in one of the rare cases when the complete set of affine invariants is known: for the two-step nilpotent Lie algebras with the two-dimensional center. Informally speaking, we prove that such a Lie algebra is an Einstein nilradical, if it is defined by a matrix pencil having no nilpotent blocks in the canonical form and no elementary divisors of a very high multiplicity. We also discuss the connection between the property of a two-step nilpotent Lie algebra and its dual to be an Einstein nilradical. | |
| dc.description | 16 pages | |
| dc.identifier | https://arxiv.org/abs/0805.0646 | |
| dc.identifier | http://arxiv.org/abs/0805.0646 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/160388 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C30; 53C25 | |
| dc.title | Einstein solvmanifolds attached to two-step nilradicals | |
| dc.type | text |