Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)



Einstein solvmanifolds and the pre-Einstein derivation

Author: Y. Nikolayevsky
Journal: Trans. Amer. Math. Soc. 363 (2011), 3935-3958
MSC (2000): Primary 53C30, 53C25
Published electronically: March 10, 2011
MathSciNet review: 2792974
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: An Einstein nilradical is a nilpotent Lie algebra which can be the nilradical of a metric Einstein solvable Lie algebra. The classification of Riemannian Einstein solvmanifolds (possibly, of all noncompact homogeneous Einstein spaces) can be reduced to determining which nilpotent Lie algebras are Einstein nilradicals and to finding, for every Einstein nilradical, its Einstein metric solvable extension. For every nilpotent Lie algebra, we construct an (essentially unique) derivation, the pre-Einstein derivation, the solvable extension by which may carry an Einstein inner product. Using the pre-Einstein derivation, we then give a variational characterization of Einstein nilradicals. As an application, we prove an easy-to-check convex geometry condition for a nilpotent Lie algebra with a nice basis to be an Einstein nilradical and also show that a typical two-step nilpotent Lie algebra is an Einstein nilradical.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 53C30, 53C25

Retrieve articles in all journals with MSC (2000): 53C30, 53C25

Additional Information

Y. Nikolayevsky
Affiliation: Department of Mathematics, La Trobe University, Victoria, 3086, Australia

Keywords: Einstein solvmanifold, Einstein nilradical
Received by editor(s): March 31, 2008
Received by editor(s) in revised form: March 10, 2009
Published electronically: March 10, 2011
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia