INVESTIGADORES
FERNANDEZ CULMA Edison Alberto
artículos
Título:
Classification of 7-dimensional Einstein nilradicals
Autor/es:
EDISON ALBERTO FERNÁNDEZ CULMA
Revista:
TRANSFORMATION GROUPS
Editorial:
BIRKHAUSER BOSTON INC
Referencias:
Lugar: Massachusetts; Año: 2012 vol. 17 p. 639 - 656
ISSN:
1083-4362
Resumen:
The problem of classifying Einstein solvmanifolds, or equivalently, Ricci soliton nilmanifolds, is known to be equivalent to a question on the variety $mathfrak{N}_n(CC)$ of $n$-dimensional complex nilpotent Lie algebra laws. Namely, one has to determine which $mathrm{GL}_n(CC)$-orbits in $mathfrak{N}_n(CC)$ have a critical point of the squared norm of the moment map. In this paper, we give a classification result of such distinguished orbits for $n = 7$. The set $mathfrak{N}_7(CC) / mathrm{GL}_7(CC)$ is formed by $148$ nilpotent Lie algebras and $6$ one-parameter families of pairwise non-isomorphic nilpotent Lie algebras. We have applied to each Lie algebra one of three main techniques to decide whether it has a distinguished orbit or not.
