Classification of 7-dimensional Einstein nilradicals

Abstract

The problem of classifying Einstein solvmanifolds, or equivalently, Ricci soliton nilmanifolds, is known to be equivalent to a question on the variety of n-dimensional complex nilpotent Lie algebra laws. Namely, one has to determine which GL(n)-orbits in this variety have a critical point of the squared norm of the moment map. In dimension 7, there are 148 complex nilpotent Lie algebras and 6 curves of pairwise non-isomorphic nilpotent Lie algebras, and we give in this paper a complete classification of the aforementioned distinguished orbits.

18 pages. References and Comments added. Final version

References in corpus (1)

• Classification of 7-dimensional Einstein nilradicals

Cited by in corpus (8)

• Classification of 7-dimensional Einstein nilradicals
• Classification of Nilsoliton metrics in dimension seven
• Construction of nice nilpotent Lie groups
• Three-dimensional solvsolitons and the minimality of the corresponding submanifolds
• Classification of Ordered Type Soliton Metric Lie Algebras by a Computational Approach
• Laplacian flow of closed $G_2$-structures inducing nilsolitons
• The topology of the set of nonsoliton Lie algebras in the moduli space of nilpotent Lie algebras
• On $G_2$-structures, special metrics and related flows