Nice pseudo-Riemannian nilsolitons

Abstract

We study nice nilpotent Lie algebras admitting a diagonal nilsoliton metric. We classify nice Riemannian nilsolitons up to dimension $9$. For general signature, we show that determining whether a nilpotent nice Lie algebra admits a nilsoliton metric reduces to a linear problem together with a system of as many polynomial equations as the corank of the root matrix. We classify nice nilsolitons of any signature: in dimension $\le 7$; in dimension $8$ for corank $\le 1$; in dimension $9$ for corank zero.

Article: 28 pages, 8 tables. Ancillary file: 98 pages, 4 tables

References in corpus (5)

• Ricci-flat and Einstein pseudoriemannian nilmanifolds
• Construction of nice nilpotent Lie groups
• Indefinite Einstein metrics on nice Lie groups
• Wick-rotations of pseudo-Riemannian Lie groups
• Indefinite nilsolitons and Einstein solvmanifolds